hyph-compounds.txt

model structure: 49
model category: 47
tensor product: 42
factorization system: 28
vector space: 28
category theory: 25
Kan extension: 23
vector bundle: 19
$ omega $ - category: 18
equivalence relation: 17
homotopy category: 17
abelian group: 17
homotopy theory: 17
Hopf algebra: 16
model category structure: 15
category structure: 15
descent morphism: 15
finite limit: 14
Hausdorff space: 14
base category: 13
Galois theory: 13
Maltsev category: 12
Grothendieck topos: 11
homotopy type: 11
$ c $ - system: 11
transition system: 10
group action: 9
chain complex: 9
finite set: 9
Markov process: 9
Gray - category: 8
functor category: 8
closure operator: 8
homotopy equivalence: 8
realizability topos: 8
Frobenius algebra: 7
Morita equivalence: 7
Frobenius object: 7
field theory: 7
algebra structure: 7
Linear Logic: 7
descent theory: 7
coherence condition: 7
topos theory: 7
quotient map: 7
lie algebra: 7
omega - category: 7
action core: 7
Fermat theory: 7
abelian category: 6
Lawvere theory: 6
$ v $ - category: 6
homology theory: 6
linear functor: 6
Lie algebra: 6
Variety Theorem: 6
restriction category: 6
unit action: 6
Euler characteristic: 6
tensor category: 5
slice category: 5
finite product: 5
cohomology class: 5
Chu construction: 5
module category: 5
coherence theorem: 5
$ n $ - category: 5
$ r $ - module: 5
ground category: 5
Eilenberg - Moore algebra: 5
Moore algebra: 5
Cauchy completion: 5
Moore category: 5
sup - lattice: 5
Algebraic Topology: 5
Feynman diagram: 5
Chu - span: 5
$ c^* $ - algebra: 5
map category: 5
probability distribution: 5
homotopy colimit: 5
Frobenius monoid: 5
lie groupoid: 5
vector lattice: 5
$ (pi, lambda) $ - structure: 5
$ j $ - theory: 5
finite group: 4
enchilada category: 4
proof net: 4
quantum field theory: 4
Eilenberg - Moore object: 4
Moore object: 4
homotopy group: 4
linear logic: 4
MD - sketch: 4
Chu category: 4
nerve functor: 4
semidirect product: 4
Mackey functor: 4
lie group: 4
Maltsev variety: 4
KZ - doctrine: 4
object analogue: 4
quantum group: 4
presheaf topos: 4
hopf monad: 4
Hopf monad: 4
et cetera: 4
Yang - Baxter equation: 4
Baxter equation: 4
oplax morphism: 4
Stone space: 4
characterization theorem: 4
$ a_infty $ - category: 4
surface holonomy: 4
module structure: 4
approach space: 4
Hecke algebra: 4
Hilbert space: 4
homotopy invariant: 4
chain rule: 4
Reidemeister trace: 4
skew monoidale: 4
Tannaka duality: 4
wreath product: 4
smash product: 4
equivalence class: 4
$ infty $ - groupoid: 4
category functor: 4
$ a_infty $ - algebra: 4
flow diagram: 4
linear relation: 4
Frobenius structure: 4
sup lattice: 4
hopf monoid: 4
Bousfield localization: 3
infinity - category: 3
lie - rinehart: 3
persistence module: 3
base topos: 3
identity functor: 3
adjoint string: 3
$ q $ - module: 3
homotopy pushout: 3
de Paiva: 3
Intuitionistic Linear Logic: 3
coherence result: 3
loop space: 3
$ kz $ - doctrine: 3
cell complex: 3
$ omega $ - complex: 3
Chu - construction: 3
ring theory: 3
lambda calculus: 3
number object: 3
Frobenius law: 3
quasi -: 3
cat - group: 3
Grothendieck topology: 3
branching homology: 3
finite ordinal: 3
$ omega $ - graph: 3
Kan condition: 3
ramification groupoid: 3
hopf algebra: 3
Stone duality: 3
information system: 3
EA sketch: 3
amalgamation property: 3
subobject classifier: 3
linear setting: 3
model theory: 3
Birkhoff subcategory: 3
Eilenberg - Moore category: 3
Morita equivalent: 3
$ f $ - algebra: 3
$ (t, v) $ - algebra: 3
copower object: 3
harmonic oscillator: 3
stuff type: 3
base space: 3
representation theory: 3
cyclic spectrum: 3
$ mathcal{q} $ - category: 3
$ d $ - translation: 3
Dialectica construction: 3
monad morphism: 3
core algebra: 3
$ g $ - set: 3
$ a_infty $ - functor: 3
Maltsev operation: 3
Tambara module: 3
linear map: 3
vector field: 3
Elementary Linear Logic: 3
deformation theory: 3
paste diagram: 3
diagram lemma: 3
Mac Lane: 3
Möbius category: 3
Möbius interval: 3
order chain rule: 3
bi - module: 3
range category: 3
factorisation system: 3
monoidal functor: 3
string diagram: 3
co - smash product: 3
Schonfinkel algebra: 3
Gray tensor product: 3
Grothendieck completion: 3
duoidal category: 3
stability property: 3
value measure: 3
$ infty $ - algebra: 3
codescent object: 3
bi - compactification: 3
universe category functor: 3
Dedekind completion: 3
product structure: 3
snail lemma: 3
Huq commutator: 3
Maltsev object: 3
bimonoidal functor: 3
Levi category: 3
cofibration category: 3
Picard - Vessiot ring: 3
Vessiot ring: 3
Kan - injectivity: 3
Witt vector: 3
$ (p, tilde{p}) $ - structure: 3
isotropy group: 3
tube algebra: 3
pullback complement: 3
word problem: 2
product functor: 2
Galois structure: 2
discrete space: 2
dimension one: 2
target category: 2
inference rule: 2
petit topos: 2
way site: 2
adjoint monad: 2
Frobenius pseudomonoid: 2
pseudo ambijunction: 2
$ s $ - homotopy: 2
cofibrant homotopy: 2
dihomotopy equivalence: 2
Grothendieck topo: 2
algebra morphism: 2
property - like: 2
cell composition: 2
cw - complex: 2
group case: 2
colimit specification: 2
inclusion functor: 2
mapping cone: 2
convolution product: 2
Harrison cohomology: 2
Quillen cohomology: 2
datum - specification: 2
order structure: 2
duality theory: 2
Moore complex: 2
finite sum: 2
star - autonomous: 2
K"{u}nneth formulae: 2
Hausdorff group: 2
convergence relation: 2
ultrafilter monad: 2
category $ a $: 2
decision procedure: 2
semiprime ring: 2
$ v $ - theory: 2
$ v $ - monad: 2
Church - Rosser: 2
coherence problem: 2
semigroup theory: 2
domain theory: 2
powerset functor: 2
homotopy relation: 2
$ r{cal o}(g, x) $ - module: 2
Dedekind category: 2
branched cover: 2
$ g $ - space: 2
diagram category: 2
closure space: 2
finite - limit: 2
execution path: 2
branching side: 2
Mackey coreflection: 2
$ theta $ - category: 2
$ cal d $ - colimit: 2
Kan complex: 2
point constructor: 2
braid group: 2
Scott topology: 2
powerdomain construction: 2
finite colimit: 2
homotopy kernel: 2
entropic category: 2
comprehension calculus: 2
$ v $ - functor: 2
Goguen category: 2
unit interval: 2
injectivity class: 2
van Kampen: 2
codescent morphism: 2
preservation property: 2
paper study: 2
domain bicategory: 2
proarrow equipment: 2
type condition: 2
distribution theory: 2
exactness property: 2
Tychonoff space: 2
product construction: 2
Azumaya algebra: 2
Galois extension: 2
Wirthmuller isomorphism: 2
companion paper: 2
Brian Day: 2
exactness condition: 2
Baer invariant: 2
Kleisli category: 2
$ sl $ - monoid: 2
$ t $ - algebra: 2
cohomology group: 2
von Neumann: 2
cohomology functor: 2
Isbell adjunction: 2
Cauchy filter: 2
Yoneda completion: 2
$ set $ - monad: 2
homotopy groupoid: 2
Philip Higgins: 2
span construction: 2
base quantaloid: 2
adjoint functor: 2
Directed Algebraic Topology: 2
power object: 2
disjoint union: 2
gauge theory: 2
non -: 2
Yoneda - system: 2
kernel - cokernel lemma: 2
cokernel lemma: 2
Bourn localization: 2
Jónsson - Tarski variety: 2
Tarski variety: 2
filler condition: 2
unital ring: 2
Chu - spans: 2
computer science: 2
Formal Concept Analysis: 2
Concept Analysis: 2
approximable concept: 2
deduction formulation: 2
ring object: 2
gerbe module: 2
bundle gerbes: 2
comprehension scheme: 2
product monad: 2
ball functor: 2
non - cohesion: 2
quality type: 2
base change: 2
Brauer group: 2
Kleisli bicategory: 2
representable functor: 2
adjoint arrow: 2
$ v $ - relation: 2
$ d $ - space: 2
derivation type: 2
tangent bundle: 2
base field: 2
shape equivalence: 2
state space: 2
Alster condition: 2
pasting diagram: 2
abelian object: 2
Snake Lemma: 2
Galois descent: 2
bimonoidal category: 2
Dynkin diagram: 2
Hall algebra: 2
André Joyal: 2
arrow category: 2
probability monad: 2
incidence algebra: 2
isomorphism class: 2
homotopy monoid: 2
group theory: 2
basal graph: 2
type equivalence: 2
$ {cal Q} $ - category: 2
Connes fusion tensor product: 2
fusion tensor product: 2
Hilbert module: 2
comparison map: 2
$ n $ - type: 2
base ring: 2
Frobenius monoidal: 2
Monadic Equational Systems: 2
Equational Systems: 2
Equational Metalogic: 2
quotient completion: 2
Hopf module: 2
conjugation action: 2
Commutator Condition: 2
Higgins commutator: 2
Ursini commutator: 2
Smith - Pedicchio commutator: 2
Pedicchio commutator: 2
Goursat category: 2
lax functor: 2
pseudo - functor: 2
Gleason cover: 2
Crans tensor product: 2
Batanin -: 2
Yoneda embed: 2
$ ell $ - algebra: 2
tuple groupoid: 2
iteration pseudomonad: 2
codensity monad: 2
combinatory algebra: 2
fibration structure: 2
homotopy bicategory: 2
lifting property: 2
MacNeille completion: 2
$ infty $ - homotopie: 2
mapping space: 2
$ t_0 $ - space: 2
mutation pair: 2
groupoid action: 2
wiring diagram: 2
commute action: 2
coalgebra - like: 2
transformation groupoid: 2
group $ g $: 2
adjoint action: 2
surface holonomie: 2
ann - category: 2
bimodule butterfly: 2
covering space: 2
path space: 2
group structure: 2
cospan category: 2
linear category: 2
split extension classifier: 2
extension classifier: 2
control theory: 2
Segal group: 2
Segal group action: 2
$ q $ - category: 2
coherence property: 2
action accessibility: 2
Eilenberg - Moore: 2
proximity Dedekind vector lattice: 2
Dedekind vector lattice: 2
snake lemma: 2
Bousfield delocalization: 2
biadjoint triangle: 2
adjoint triangle: 2
pseudo - Kan extension: 2
$ a $ - module: 2
co - Maltsev: 2
action representability: 2
invertibility hypothesis: 2
$ d $ - ideal: 2
meet - semilattice: 2
$ sm $ - ideal: 2
Artin - Mazur codiagonal: 2
Mazur codiagonal: 2
functor calculus: 2
pseudo - monoid: 2
$ g $ - uniformity: 2
ind - category: 2
Tangent Structure: 2
tangent functor: 2
truncation poset: 2
split monomorphism: 2
$ (infty, 1) $ - category: 2
group object: 2
mutation mechanism: 2
dg vector space: 2
quantum category: 2
tangent category: 2
ESN Theorem: 2
box functor: 2
circuit diagram: 2
stability result: 2
$ q $ - distributor: 2
Brauer - Clifford group: 2
Clifford group: 2
pinwheel problem: 1
colimit argument: 1
Reshetikhin - Turaev theory: 1
Turaev theory: 1
fusion category: 1
group orbifold: 1
Turaev - Viro state sum construction: 1
Viro state sum construction: 1
state sum construction: 1
sum construction: 1
ribbon tensor category: 1
Tambara - Yamagami: 1
extension map: 1
Chevalley criterion: 1
category $ etop $: 1
Nerve functor: 1
Baum - Connes conjecture: 1
Connes conjecture: 1
inverting equivalence: 1
motivating application: 1
$ k $ - homology: 1
infinity - category theory: 1
pretorsion theory: 1
Alexandroff - discrete space: 1
multi - source: 1
yoneda structure: 1
category coincide: 1
coend formula: 1
Gamma - set: 1
$ s $ - module: 1
archimedean place: 1
structure sheaf: 1
Gromov norm: 1
Riemann surface: 1
morphism category: 1
world datum: 1
homology functor: 1
rank function: 1
persistence function: 1
persistence diagram: 1
bottleneck distance: 1
point cloud datum: 1
cloud datum: 1
$ infty $ - topos $ e $: 1
topos $ e $: 1
homotopy invariance: 1
Lusternik - Schnirelmann category: 1
Schnirelmann category: 1
Boolean Logic: 1
generating class $ s $: 1
class $ s $: 1
gro topos: 1
idempotent identity: 1
site criterion: 1
2D topological: 1
2D TQFT: 1
category $ m $: 1
dihomotopy relation: 1
non point: 1
monad property: 1
lax - idempotent: 1
cauchy - completion: 1
Cauchy - completeness: 1
sub - bicategory: 1
$ [n, m] $ - equivalence: 1
CW - complex: 1
homotopy class: 1
$ k $ - multilinearity: 1
$ k $ - model: 1
limit specification: 1
sketch commute: 1
sketch model: 1
finite coproduct: 1
Bianchi Identity: 1
groupoid theory: 1
Homotopy Addition Lemma: 1
Addition Lemma: 1
gauge group bundle: 1
group bundle: 1
Van Kampen type: 1
Kampen type: 1
infinite loopspace machine: 1
loopspace machine: 1
Left Kan extension: 1
promonoidal functor: 1
non associative: 1
disjunction operation: 1
non commutative: 1
M Barr: 1
account torsion: 1
presheaf category: 1
Finite Sum sketch: 1
Sum sketch: 1
medial rule: 1
deduction rule: 1
coherence space: 1
functor $ cal p $: 1
string distributive: 1
coproduct specification: 1
homotopy module: 1
tensor - par fragment: 1
par fragment: 1
Bilinear Logic: 1
FILL category: 1
MIX rule: 1
$ k $ - theory: 1
order sentence: 1
Ed Keenan: 1
finite model: 1
th term: 1
category $ cat a $: 1
boolean algebra structure: 1
image map: 1
construction datum: 1
commutator subgroup: 1
arrow equipment: 1
equipment arrow: 1
Whitehead Theorem: 1
parity complex: 1
$ omeg $ - complex: 1
CW complex: 1
cohomology theory: 1
Mackey functor category: 1
group algebra: 1
ultrafilter functor: 1
unit law: 1
Gray - category $ a $: 1
connection pair: 1
torsion - freeness: 1
bf Walk: 1
discrete Conduché: 1
F. Lamarche: 1
correctness criterion: 1
finite limit coincide: 1
limit coincide: 1
numerical function: 1
series expansion: 1
Stirling function: 1
type term constructor: 1
term constructor: 1
lambda calculi: 1
product type: 1
Maltsev operator: 1
ground Church - Rosser: 1
ground CR: 1
endomorphism monoid: 1
J. - Y. Girard: 1
Y. Girard: 1
self - similarity: 1
Chu object: 1
lattice dual: 1
Phoa principle: 1
overt discrete space: 1
Dwyer - Kan: 1
cylinder object: 1
static module: 1
non - topos theorist: 1
topos theorist: 1
filter ring: 1
$ rbbb{c} $ - module: 1
kernel - congruence: 1
$ omega $ - group: 1
congruence - modular: 1
base functor: 1
$ {cal v} $ - category: 1
$ {cal v}^{op} $ - category: 1
Joyal - Tierney theorem: 1
Tierney theorem: 1
dedekind category: 1
relation algebra: 1
side condition: 1
cartesian closure: 1
pseudo equivalence relation: 1
sheaf theory: 1
finite loop space: 1
Barr exact: 1
Commutator theory: 1
branching area: 1
sub - complex: 1
invariance result: 1
merging side: 1
merge area: 1
category $ alg $: 1
finite disk: 1
graph be: 1
category simple: 1
$ omega $ - functor: 1
bi - quotient map: 1
colimit completion: 1
postnikov complex: 1
Postnikov complex: 1
horn - lift: 1
alternation hierarchy problem: 1
hierarchy problem: 1
alternation hierarchy: 1
$ mu $ - lattice: 1
lattice operation: 1
Barr exactness assumption: 1
exactness assumption: 1
Hurwitz action: 1
path groupoid: 1
Artin group: 1
linear ordering: 1
Dehornoy ordering: 1
identity element: 1
Artin representation: 1
rewrite system: 1
abelian sheaf cohomology: 1
sheaf cohomology: 1
Cech cohomology: 1
cofibre sequence: 1
Gabriel - Ulmer duality: 1
Ulmer duality: 1
Lawvere - rosicky: 1
Morita duality: 1
Laplace operator: 1
category Opmon: 1
$ m $ - subobject: 1
structure entropic category: 1
cut - elimination: 1
Tannaka - Krein reconstruction: 1
Krein reconstruction: 1
self - adjoint exponential: 1
adjoint exponential: 1
subspace topology: 1
locale theory: 1
Sober Spaces: 1
functor $ cal{a} to cal{b} $: 1
Stone representation: 1
Algebraic Topology study: 1
Topology study: 1
traffic network: 1
space - time model: 1
time model: 1
homotopy fibre: 1
fibre sequence: 1
$ lambda $ - calculus: 1
reversibility notion: 1
sub - category: 1
$ l $ - colocalization: 1
$ l $ - localization: 1
A. K. Bousfield: 1
K. Bousfield: 1
colocalization process: 1
chain functor: 1
monad $ (( - )^2, i, c) $: 1
pseudo - algebra structure: 1
cut elimination: 1
Whitman theorem: 1
proof theory: 1
player input - output game: 1
input - output game: 1
output game: 1
derive functor: 1
Lie algebra homology: 1
algebra homology: 1
ground ring: 1
hopf formula: 1
lie epimorphism: 1
entity - Relationship - Attribute idea: 1
Relationship - Attribute idea: 1
Attribute idea: 1
design process: 1
finite - sum sketch: 1
sum sketch: 1
query language: 1
groupoid correspond: 1
Lie algebras: 1
Steiner quasi: 1
heyte algebra: 1
composition - representative: 1
composition - representability: 1
decomposition result: 1
cell component: 1
module bicategory: 1
Beck - Chevalley - type condition: 1
Chevalley - type condition: 1
$ (t, v) $ - algebras: 1
wave equation: 1
limit construction: 1
$ cr $ - epimorphism: 1
$ z $ - ideal: 1
homotopy classification: 1
classification theorem: 1
ring - group: 1
Clifford system: 1
factor set: 1
product projection: 1
invariance theorem: 1
ary term: 1
precubical set: 1
composition law: 1
element conjecture: 1
Grothendieck isomorphism theorem: 1
isomorphism theorem: 1
Linear bicategorie: 1
cell level: 1
lax transformation: 1
poly - module: 1
quasigroup isotopie: 1
quasigroup model theory: 1
multiplication map: 1
inverse $ x' $: 1
group cohomology: 1
identity object: 1
Chern - Simons theory: 1
Simons theory: 1
category 2vect: 1
bilinear functor: 1
Jacobi identity: 1
Zamolodchikov tetrahedron equation: 1
tetrahedron equation: 1
semistrict Lie: 1
term $ l_infty $ - algebra: 1
$ l_infty $ - algebra: 1
Lie algebra cohomology: 1
algebra cohomology: 1
parameter family: 1
powerlocale construction: 1
Sierpinski locale: 1
geometricity result: 1
locale presentation: 1
category c: 1
Cassidy - Héebert - Kelly factorization: 1
Héebert - Kelly factorization: 1
Kelly factorization: 1
$ v $ - Cat: 1
$ v $ - module: 1
preservation theorem: 1
category $ b $: 1
Baer Extension Theory: 1
Extension Theory: 1
size restriction: 1
finite diagram: 1
fashion notion: 1
multilimit merging functor: 1
merging functor: 1
site structure: 1
pretopos completion process: 1
completion process: 1
finite limit property: 1
limit property: 1
approximation technique: 1
approximation result: 1
cotriple homology theory: 1
Stallings - Stammbach sequence: 1
Stammbach sequence: 1
group homology: 1
Furtado - Coelho: 1
kernel pair: 1
CCD lattice characterization: 1
lattice characterization: 1
combinatorial topos: 1
finite automata: 1
compatibility condition: 1
coalgebra structure: 1
similarity strict: 1
homotopy kernels: 1
$ v $ - matrix: 1
finite spectra: 1
$ sigma $ - algebra: 1
quotient algebra: 1
Jan Reiterman: 1
colimit commute: 1
class $ phi^ - $: 1
limit commute: 1
Cauchy - completion: 1
Morita theorem: 1
self - distance law: 1
distance law: 1
triangle inequality: 1
netwise form: 1
Baues - Jibladze descent: 1
Jibladze descent: 1
$ (P, V) $ - algebra: 1
powerset monad: 1
General Coalgebra: 1
monoid monad: 1
semigroup monad: 1
Physical Traces: 1
Yanking axiom: 1
machine code: 1
term judgement: 1
coherence requirement: 1
op - Grothendieck construction: 1
Grothendieck construction: 1
type constructor: 1
push - value: 1
chain complexe: 1
unit morphism: 1
$ n $ - simplice: 1
epic von Neumann: 1
$ sigma $ - family: 1
$ sigma $ - automata: 1
Basic Intuitionistic Set Theory: 1
Intuitionistic Set Theory: 1
Set Theory: 1
sheaf model: 1
Basic Intuitionistic Class Theory: 1
Intuitionistic Class Theory: 1
Class Theory: 1
class theory: 1
epimorphism topology: 1
homology isomorphism: 1
homotopy extension property: 1
extension property: 1
factorization monad: 1
potency object: 1
Burnside rig: 1
quantum mechanic: 1
stuff operator: 1
circle group: 1
$ m $ - stuff type: 1
time evolution: 1
combinatorial setting: 1
Feynman rule: 1
Serge Bouc: 1
permutation representation: 1
category theorist: 1
transition function: 1
connection form: 1
curvature form: 1
nonflat connection: 1
Ambrose - Singer: 1
component category: 1
Category Theory: 1
chu category: 1
$ omega $ - category monad: 1
category monad: 1
paper equivalence: 1
ana - bicategory: 1
2D - multitopic category: 1
multitopic category: 1
FOLDS equivalence: 1
FOLDS - specification: 1
restriction homomorphism: 1
sub - semilattice: 1
adjoint construction: 1
object part: 1
$ fc $ - multicategorie: 1
TFT construction: 1
cross cap constraint: 1
cap constraint: 1
semilattice fibration: 1
category determine: 1
$ mathcal{q} $ - module: 1
class $ mathbb{c} $: 1
comma - category $ (mathcal{d}downarrow a) $: 1
category $ (mathcal{d}downarrow a) $: 1
orthomodular lattice: 1
specialization order: 1
$ k $ - quiver: 1
functor $ a_infty(fq, a) to a_1(q, a) $: 1
quiver $ q to a $: 1
face operation: 1
$ t $ - complex: 1
chain homotopie: 1
descent type: 1
algebra functor: 1
descent theorem: 1
Dialectica - style interpretation: 1
style interpretation: 1
affine logic: 1
order formula: 1
dialectica category: 1
order setting: 1
$ ?clik $ - translation: 1
translation result: 1
$ existsforall $ - formula: 1
negation translation: 1
cell - span: 1
base bicategory: 1
state transition system: 1
cyclic Chu - span: 1
meeting point: 1
Chu Spaces: 1
Domain Theory: 1
finite Chu space: 1
Chu space: 1
relation correspond: 1
association rule: 1
Scott domain: 1
approximable mapping: 1
Full Intuitionistic Linear Logic: 1
calculus formulation: 1
deduction system: 1
term assignment system: 1
assignment system: 1
involution $ ( - )^{ } $: 1
identity arrow: 1
Segal condition: 1
Moerdijk - Weiss: 1
$ omega $ - operad: 1
endo - 2: 1
algebra condition: 1
co)homology functor: 1
cohomotopy functor: 1
model enrichment: 1
endomorphism ring object: 1
endomorphism ring: 1
adjoint module: 1
$ t $ - operation: 1
$ s $ - operation: 1
Hopf algebra structure: 1
product operad: 1
factor operad: 1
transposition symmetry: 1
definition composition: 1
$ k $ - cell: 1
k - cobordisms: 1
bundle gerbe module: 1
Michael covering: 1
dominance domain: 1
topos doctrine: 1
Core algebra: 1
quotient monad: 1
sequel paper: 1
monad approximation: 1
Francisco Marmolejo: 1
coproduct completion: 1
function space: 1
state sum invariant: 1
sum invariant: 1
Dijkgraaf - Witten Invariant: 1
Witten Invariant: 1
unit - ball functor: 1
unit ball functor: 1
Banach space: 1
Abramsky - Jagadeesan games: 1
Jagadeesan games: 1
player game: 1
Olivier Laurent: 1
adjoint connection: 1
module - equivalence: 1
sheaf - equivalence: 1
formula $ (downarrow p)x = Gamma_clik(x/p) $: 1
complement operator: 1
cohomology ring: 1
cohesive background: 1
quality form: 1
Grothendieck condition VII: 1
condition VII: 1
ring homomorphism: 1
base change functor: 1
change functor: 1
pseudo - monad: 1
pseudo - slice: 1
Grothendieck derivator: 1
Frobenius operation: 1
finite space: 1
affine space: 1
1 +: 1
function algebra: 1
dimension rig: 1
$ a_infty $ - subcategory: 1
functor $ a mapsto a_infty^u(c, a)_{mod b} $: 1
unital $ a_infty $ - functor $ c to a $: 1
$ a_infty $ - functor $ c to a $: 1
functor $ c to a $: 1
$ k $ - module: 1
coalgebra object: 1
$ d $ - coalgebra: 1
stability law: 1
arrow interval: 1
hom - set: 1
Linear Abadi: 1
Plotkin Logic: 1
domain equation: 1
LAPL structure: 1
pushout topos: 1
connectedness assumption: 1
Galois topos: 1
Absolute Kan extension: 1
fortiori protomodular: 1
classification table: 1
Baer sum: 1
comonoid homomorphism: 1
identity map: 1
Maltsev co: 1
identity morphism: 1
Yoneda embedding: 1
functor modulo group: 1
modulo group: 1
monad functor: 1
graph structure: 1
affine object: 1
point set: 1
Daisuke Tambara: 1
category $ da $: 1
coalgebra modality: 1
linear notion: 1
term calculus: 1
$ m $ - algebra: 1
algebra $ (a, a) $: 1
algebra $ (MA_0, m) $: 1
space colimit: 1
homotopy type functor: 1
type functor: 1
abelian categorification: 1
weight category: 1
quantum link invariant: 1
link invariant: 1
link homology: 1
finite derivation type: 1
convergent presentation: 1
stack exist: 1
Morse Theory: 1
profinite group: 1
finite discrete: 1
$ z $ - module: 1
generator embed: 1
adjoint morphism: 1
Hilbert category: 1
2 - Hilbert space: 1
Jon Beck: 1
wreath product monad: 1
Seely category: 1
ANR - space: 1
homotopy orthogonality: 1
high Homotopy van Kampen Theorems: 1
Homotopy van Kampen Theorems: 1
van Kampen Theorems: 1
Kampen Theorems: 1
colimit calculation: 1
base point: 1
briefly application: 1
control flow: 1
state space split: 1
space split: 1
machine behavior: 1
program analysis: 1
slice - category construction: 1
category construction: 1
plank construction: 1
Dieudonne construction: 1
Lindelof case: 1
neighbourhood property: 1
p - space: 1
Lindelof CNP space: 1
CNP space: 1
Alster space: 1
adjoint couple: 1
projection formula: 1
composition formula: 1
duality preserve: 1
push -: 1
Witt group: 1
co)endomorphism algebra: 1
von Neumann core: 1
Neumann core: 1
$ g $ - algebra: 1
counter - example: 1
subobject functor: 1
reflection property: 1
Charles Ehresmann: 1
jet tangent: 1
Split Short Five Lemma: 1
Short Five Lemma: 1
Five Lemma: 1
commutator condition: 1
third cohomology group: 1
Non - abelian Snake Lemma: 1
abelian Snake Lemma: 1
completeness /: 1
cocompleteness assumption: 1
module corresponding: 1
star - multiplicative: 1
$ omega_2 $ - group: 1
Galois descent theory: 1
Grothendieck descent: 1
Grothendieck descent data coincide: 1
descent data coincide: 1
data coincide: 1
Grothendieck descent theory: 1
descent construction: 1
abelian cohomology: 1
category $ cat(e) $: 1
$ b $ - torsor: 1
Cech cocycle: 1
Hopf formulae: 1
protoadditive functor: 1
preservation yield: 1
product measure: 1
object biadjunction: 1
commutation relation: 1
field operator: 1
deformation parameter: 1
finite field: 1
Schreier - Mac Lane extension: 1
Mac Lane extension: 1
Lane extension: 1
Schreier - Mac Lane: 1
Galois groupoid: 1
Span construction: 1
truth - value: 1
power set monad: 1
set monad: 1
CCD sup - lattice: 1
Möbius inversion principle: 1
inversion principle: 1
inversion result: 1
direction follow: 1
kernel object: 1
K - theory: 1
Waldhausen subcategory: 1
John Baez: 1
James Dolan: 1
semigroup action: 1
semigroup prehomomorphism: 1
tensor product functor: 1
Lawvere - product: 1
extension system: 1
extension system work: 1
system work: 1
incompleteness result: 1
Cayley graph: 1
combinatorial group theory: 1
graph morphism: 1
zeta series: 1
walk space: 1
restriction structure: 1
completion operation: 1
Zariski topology: 1
exponentiability characterization: 1
uniform space: 1
$ omega $ - loop: 1
bundle category: 1
Faà di Bruno: 1
di Bruno: 1
order chain rule fibration: 1
chain rule fibration: 1
rule fibration: 1
coherence issue: 1
subobject classifier axiom: 1
classifier axiom: 1
Cattani - Sassone: 1
orthogonality class: 1
process algebra: 1
Cauchy completion monad: 1
completion monad: 1
symmetrisation comonad: 1
Cauchy - bilateral: 1
chain - complex: 1
term lie infinity algebra: 1
lie infinity algebra: 1
infinity algebra: 1
quantum algebra: 1
Wiener algebra: 1
analysis term: 1
test object: 1
communicating system: 1
Computer Science: 1
knot colouring: 1
bi - finite: 1
von Neumann algebra: 1
Neumann algebra: 1
Hilbert bi - module: 1
loop group: 1
unit map: 1
Quantum category: 1
category unpack: 1
quantum structure: 1
site characterization: 1
lax adjunction: 1
Artin - Wraith glueing: 1
Wraith glueing: 1
etale groupoid: 1
number vanishe: 1
string diagram calculus: 1
diagram calculus: 1
Explicit Basis property: 1
Basis property: 1
Grothendieck site $ (c, j) $: 1
site $ (c, j) $: 1
Yoneda Lemma: 1
Model Theory: 1
sphere spectrum: 1
Vitale model: 1
Postnikov datum: 1
graphlike structure: 1
term logic: 1
part paper: 1
Boris Schein: 1
Freyd conjecture: 1
Kornel Szlachanyi: 1
skew pseudo: 1
base comonoid: 1
quantum groupoid: 1
biadjoint biequivalence: 1
po - monoid: 1
congruence lattice: 1
cell complexe: 1
Richard Garner: 1
pre - hopf: 1
fusion operator: 1
pre - hopf monad: 1
Galois entwining: 1
section application: 1
fibre functor: 1
Frobenius monoidal functor: 1
cocategory object: 1
Hopf comonad coincide: 1
comonad coincide: 1
Schwartz distribution: 1
building block: 1
wreath product construction: 1
category $ wdl^{(n)}(cal k) $: 1
$ (n+1) $ - tuple: 1
monad $ mnd $: 1
functor $ wdl^{(n)}(ock)to wdl^{(n - 1)}(overline cal k) $: 1
associativity property: 1
Ising type quantum spin chain: 1
type quantum spin chain: 1
quantum spin chain: 1
spin chain: 1
algebra % construction: 1
% construction: 1
Monadic Equational Systems satisfie: 1
Equational Systems satisfie: 1
Systems satisfie: 1
completeness property: 1
force extensionality: 1
comodule - monad: 1
algebra - comonoid: 1
Hopf algebra literature: 1
algebra literature: 1
Hopf Galois extension: 1
interest possess: 1
extent action: 1
cross - effect: 1
category equivalence: 1
$ g $ - action: 1
other one: 1
associativity type condition: 1
Beck module: 1
$ l $ - completeness: 1
morphism concept: 1
Kuratowski - Mrówka: 1
quantale $ v $: 1
Huq property satisfy: 1
property satisfy: 1
hopf formulae: 1
abelianisation functor: 1
ary site: 1
pretopos completion: 1
push - out: 1
Kleisli object: 1
category diexact: 1
Benno van den Berg: 1
van den Berg: 1
den Berg: 1
De Morgan: 1
Herbrand realizability topos: 1
Herbrand realizability construction: 1
realizability construction: 1
operator algebra: 1
equivariant Hilbert module: 1
$ c^infty $ - superalgebra: 1
$ c^infty $ - ring: 1
category model homotopy: 1
model homotopy: 1
Maltsev axiom: 1
differentiation operation: 1
cochain complex: 1
$ (n+1) $ - category: 1
Cisinski -: 1
Isbell completion construction: 1
completion construction: 1
Isbell completion coincide: 1
completion coincide: 1
Isbell completion: 1
cocompletion functor: 1
category factor: 1
Eilenberg - Mac Lane space: 1
Mac Lane space: 1
Lane space: 1
site description: 1
sheaf topos: 1
gluing axiom: 1
framework reproduce: 1
Breen - Messing gerbes: 1
Messing gerbes: 1
abelian gerbes: 1
approach reproduce: 1
mapping class group: 1
class group: 1
Gelfand - Neumark duality: 1
Neumark duality: 1
$ c^* $ - algebras: 1
Stone - Weierstrass theorem: 1
Weierstrass theorem: 1
Gelfand ring: 1
$ {mathbb r} $ - algebra: 1
$ mathbb r $ - algebras: 1
$ * $ - algebra: 1
Yang - Baxter type equation: 1
Baxter type equation: 1
type equation: 1
$ s $ - action: 1
parameter category: 1
$ e $ - diagram: 1
iteration version: 1
monad $ ( - )^{mathbf{2}} $: 1
iteration description: 1
Kan fibration: 1
John Longley: 1
Jaap van Oosten: 1
van Oosten: 1
motivating question: 1
base semialgebra: 1
$ mathbb{j} $ - monad: 1
$ mathbb{j} $ - comonad: 1
endo - functor: 1
semiunital semimonoidal variety: 1
semimonoidal variety: 1
semiunital $ a $: 1
$ a $ - semicoring: 1
semicounitary semicomodule: 1
counital coring: 1
duality theorem: 1
bimonoid structure: 1
$ m $ - module: 1
Tannaka adjunction: 1
hom - functor: 1
hopf bimonoid: 1
strictification functor: 1
bicategory Cat: 1
Periodic Table: 1
tuply monoidal: 1
topos inclusion: 1
torsion bundle gerbe: 1
bundle gerbe: 1
Serre - Swan: 1
Lawvere - Tierney topology: 1
Tierney topology: 1
$ t $ - completion: 1
$ m $ - embedding: 1
adjoint functor factorization result: 1
functor factorization result: 1
factorization result: 1
Applegate - Tierney: 1
recognition principle: 1
Hodge complex: 1
prefactorization system: 1
$ c* $ - algebra: 1
Gelfand spectrum: 1
go result: 1
Kullback - Leibler divergence: 1
Leibler divergence: 1
probability theory: 1
measurement process: 1
enrichment base: 1
Street - Walters: 1
Leibniz type: 1
$ {infty} $ - algebra: 1
structure project: 1
Kan property: 1
$ infty $ - algebra case: 1
algebra case: 1
composition rule cite{ss07: 1
rule cite{ss07: 1
Reedy category axiom: 1
category axiom: 1
pushout - product: 1
homotopy limit: 1
vector space structure: 1
space structure: 1
rig category: 1
$ f $ - scheme: 1
Arakelov compactification: 1
path space construction: 1
space construction: 1
Grothendieck group construction: 1
group construction: 1
flow category: 1
category $ mathcal v $: 1
Morse index: 1
Morse moduli space: 1
moduli space: 1
epi - mono factorization: 1
mono factorization: 1
group representation: 1
representation $ rho $: 1
initia groupoid: 1
character formula: 1
Stone topology: 1
quotient category: 1
groupoid morphism: 1
cartesian closedness: 1
linear system: 1
elementary class: 1
limit type: 1
$ cat $ - operad: 1
comonad structure: 1
$ a_infty $ - morphism: 1
bi - inclusion: 1
Chan Hong - Mo: 1
Hong - Mo: 1
Tsou Sheung Tsun: 1
Sheung Tsun: 1
gauge covariance: 1
interchange law: 1
comparison cell: 1
kind span: 1
space theory: 1
unit disk: 1
$ c $ - covering: 1
$ pi_1(x, x_0) $ - set: 1
monodromy action: 1
$ h(c) $ - covering: 1
subgroup lattice: 1
covering category: 1
whisker topology: 1
Fan - covering: 1
quotient topology: 1
Stone - Cech compactification: 1
Cech compactification: 1
Gil de: 1
commutative Frobenius monoid: 1
Yetter - drinfel'd: 1
module coalgebra: 1
comodule algebra: 1
twisting coefficient: 1
base manifold: 1
presentation theory: 1
Day Reflection Theorem: 1
Reflection Theorem: 1
Eilenberg - Moore coalgebra: 1
Moore coalgebra: 1
quotient functor: 1
finite category: 1
Deligne 2: 1
la Hochschild - Serre: 1
Hochschild - Serre: 1
linear dual: 1
dimension hypothesis: 1
affine scheme: 1
affine ind - scheme: 1
ind - scheme: 1
indexing poset: 1
Sufficient Cohesion: 1
action theory: 1
dagger - Frobenius structure: 1
ZX - calculus: 1
$ infty $ - graph: 1
$ t^{(infty, n)} $ - algebra: 1
$ (infty, n) $ - category: 1
$ (infty, 0) $ - category: 1
Segal space model structure: 1
space model structure: 1
infinity category: 1
accessibility property: 1
accessibility rank: 1
opening section: 1