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Category Theory Glossary

The work here is based on the corpora:

  1. abstracts from the journal TAC (Theory and Applications of Categories), from 1995 up to around Dec 2020. We have 755 abstracts. This corpus is described in https://github.com/ToposInstitute/tac-corpus/.
  2. sentences extracted from the ProofNet project (https://arxiv.org/abs/2302.12433)
  3. sentences from nLab (https://github.com/ToposInstitute/nlab-corpus and https://github.com/ToposInstitute/nLab2024-corpus)
  4. sentences from the Chicago notes (kept in a different repository)

For TAC: the file tac-clean.conll contains an automatically annotated version of the corpus, with dependency structures and POS tags, obtained via spacy. The file tac-manual.conllu has an improved version, with manual cleaning of latex, to be described.

The development version of the glossary was on the Definitions in Math (DefsMath) project page.

The project changed to MathGloss and can be seen at https://mathgloss.github.io/MathGloss/

Choosing some free open source books and journals for basic Math:

  1. https://math.dartmouth.edu/~prob/prob/prob.pdf (Baez rec)
  2. https://journals.uwyo.edu/index.php/ela/issue/view/271 open source journal for LinAlg?
  3. AIM textbooks https://textbooks.aimath.org/textbooks/approved-textbooks/

Category Theory Books:

  1. Robert Goldblatt’s Topoi (originally published 1979, now a Dover pbk) a particularly helpful entry-point.

  2. a step up, Tom Leinster’s short Basic Category Theory (CUP 2014) is indeed basic and is rightly very well-regarded.

  3. Emily Riehl’s Category Theory in Context (Dover 2017)

  4. Introducing Category Theory, Peter Smith https://www.logicmatters.net/resources/pdfs/SmithCat.pdf

  5. Many lecture notes from https://www.logicmatters.net/categories/#lectures and https://www.logicmatters.net/categories/categories-lists/

particularly interesting https://math.berkeley.edu/~gbergman/245/3.2.pdf