todos.txt

- compute examples
- fix example from class (and understand it!)

- Things which we either said we'd cover, or we probably should cover:
	* the Adams isomorphism
	* the Segal conjecture
	* how do you get a Tambara functor from a ring G-spectrum?
	* how do you get an Eilenberg-Mac Lane ring G-spectrum from a Tambara functor? (this may be in
	  Ullman's paper or Strickland's notes)

- Things which need to be cleaned up:
	* RO(C_2)-graded cohomology calculations (particularly for the Burnside Mackey functor)
	* does RO(G)-graded generalized cohomology spit out Mackey functors, or just ordinary
	  cohomology?
	* what are the Eilenberg-Steenrod axioms for RO(G)-graded cohomology?

- Things which we're not going to cover, but it would be good to provide references for. Maybe it
  would be good to put this in an appendix, à la Concise Course, with a few references for each one.
	* equivariant cobordism
	* equivariant surgery theory
	* in general, how things change for compact Lie groups
	* global and motivic stuff? (i.e. there are people working on this, it relates in this way, and
	  here's a bunch of references)
	  	- for global stuff presumably Schwede's notes
	* trace methods in algebraic K-theory

- Mechanical things
	* uniformity of a name in different references in the bibliography
	* index (this currently turned off, and is a bit of a mess)
	* consistency of notation (e.g. are Mackey functors underlined?)

- Bredon cohomology treats coefficient systems as an abelian category and then just does CW
  cohomology with it. The coend is the tensor product, and the Hom is abelian-group-valued Hom.
- organized and streamlined, which it currently isn't

- idea: presheaves on the type of diagrams we have are the replacement for coefficient groups
  (namely in homology, cohomology, and EM spaces/spectra)
	* orbit category: coefficient systems, Bredon (co)homology
	* trivial family: Z[G]-modules?, Borel (co)homology
	* Burnside category (w.r.t universe): Mackey functors, RO(G)-graded cohomology theories
	* TNR bispans (w.r.t universe?): Tambara functors, ring spectra

	* how accurate is the idea that "these homotopy types are presheaves on the diagram?" (e.g.
	  Elmendorf's theorem)
	* so if you want transfers, you want the whole Burnside category... and you want transfers
	  because you want duality

Question: does such an analogy extend to Borel homotopy theory? Is there a diagram D such that
	* Borel homotopy types are Top-valued presheaves on D?
	* Borel equivariant cohomology can be taken with coefficients in Ab-valued presheaves on D?
	* generalized Borel equivariant cohomology theories are represented by Sp-valued presheaves on
	* D?

This feels like special cases of ``diagrammatic homotopy theory'' -- what general framework does
this fit into? Which theorems are formal?

random: add Dugger's quote [generalized cohomology theories] are as common as grains of sand on the
beach (p. 94 of his K-theory notes) in the section on RO(G)-graded cohomology theories.