In this video we come across about 50 online resources for category theory:
I quickly comment on about 20 major ones. I link to the university sites, arXiv sites or Amazon page - most of the mentioned books are online available.
Here's another category theory list on github
https://github.com/prathyvsh/category-theory-resources
Criteria for my book/text selection here are:
- it's a book I like
- it's a classic
- it's a book that may be taylored for particluar fields/people
- it's a book on a topic that I mentioned on my youtube channel or that's related to its content
...
(Leinster) Basic Category Theory 178
https://arxiv.org/abs/1612.09375
(Awodey) Category Theory 247
http://www.andrew.cmu.edu/course/80-413-713/notes/?C=M;O=A
(Goldblatt) Topoi: The Categorial Analysis of Logic 551
https://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/
(Simmons) An introduction to Category Theory 423
http://www.cs.man.ac.uk/~hsimmons/zCATS.pdf -- link seems to be defunkt right now
...
(MacLane) Categories for the Working Mathematician 314
https://www.amazon.com/gp/product/0387984038/ref=dbs_a_def_rwt_bibl_vppi_i0
(Pareigis) Category Theory 90
http://www.mathematik.uni-muenchen.de/~pareigis/Vorlesungen/04SS/Cats1.pdf
(Johnstone, Mehrle) Category Theory 76
http://pi.math.cornell.edu/~dmehrle/notes/partiii/cattheory_partiii_notes.pdf
(Barr, Wells) Category Theory Lecture Notes 133
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.98.9012&rep=rep1&type=pdf
...
(Smith) Category Theory - A Gentle Introduction 290
https://www.logicmatters.net/categories/
(Beaz) Category Theory Course 59
http://math.ucr.edu/home/baez/qg-winter2016/CategoryTheoryNotes.pdf
Conceptual Mathematics - A first Introduction To Categories (Lawvere, Schanuel) 375
https://www.amazon.com/Conceptual-Mathematics-First-Introduction-Categories/dp/052171916X
(Morehouse) Basic Category Theory 81
http://emorehouse.web.wesleyan.edu/research/notes/basic_category_theory.pdf
...
(Aluffi) Algebra: Chapter 0 713
https://www.amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/0821847813
(Bergman) An Invitation to General Algebraand Universal Constructions 554
https://math.berkeley.edu/~gbergman/245/3.3.pdf
(Taylor) Practical Foundations of Mathematics 580
https://www.amazon.com/Practical-Foundations-Mathematics-Cambridge-Advanced/dp/0521631076
(MacLane) Sheaves in Geometry and Logic: A First Introduction to Topos Theory
https://www.amazon.com/Sheaves-Geometry-Logic-Introduction-Universitext/dp/0387977104
(Borceux) Some glances at topos theory 63
https://tcsc.lakecomoschool.org/files/2018/06/Como2018.pdf
(Riehl) Category Theory in context 233
http://www.math.jhu.edu/~eriehl/context.pdf
(Jacobs) Categorical Logic And Type Theory 760
https://www.amazon.com/Categorical-Theory-Studies-Foundations-Mathematics/dp/0444508538
(Rodin) Axiomatic Method and Category Theory 338
https://arxiv.org/pdf/1210.1478v1.pdf
(Streicher) Introduction to Category Theory and Categorical Logic
https://www2.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf
(Paolo Perrone) Notes on Category Theory with examples from basic mathematics
https://arxiv.org/abs/1912.10642
...
(Spivak) Category Theory for Scientists 197
http://math.mit.edu/~dspivak/teaching/sp13/CT4S--static.pdf
(Fong, Spivak) Seven Sketches in Compositionality: An Invitation to Applied Category Theory 353
https://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf
(Fong, Spivak) An Invitation to Applied Category Theory 331
https://www.amazon.com/Invitation-Applied-Category-Theory-Compositionality/dp/1108711820
(Coecke, Paquette) Categories for the practising physicist 105
https://arxiv.org/pdf/0905.3010.pdf
(Milewski) Category Theory for Programmers 498
https://github.com/hmemcpy/milewski-ctfp-pdf/
(Barr, Wells) Category Theory for Computing Science 531
http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf
(Cockett) Category Theory for Computer Science 107