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Some references for category theory

To get you started on researching category theory-related subjects, here are some websites, articles and resources that contain categorical information.

Books and resources on category theory

• Awodey, Category Theory (our primary textbook)
• Riehl, Category Theory in Context
• Mac Lane, Categories for the Working Mathematician
• Borceux, Handbook of Categorical Algebra

Useful pages

• ncatlab is like a wikipedia clone specifically for category theory, algebraic topology and much more.
• math.stackexchange and mathoverflow for asking questions and/or finding answers to relatively common questions you may have about the subject. These two pages are almost identical, so keep both in mind.
• arXiv.org for open access to a good collection of academic filters – not necessarily restricted to category theory.
• researchseminars.org is a website keeping track of published research seminars, with the capability of importing into calendars etc.
• the n-category café is a blog on anything category theory related from active category theorists.
• topos institute is a collective working on mathematical science and technology. They host workshops and seminars on category theory related subjects.
• the stacks project is actually an “open source” textbook on algebraic geometry, but there is significant overlap with category theory – most notably on sheaves.
• Applied Category Theory conference is a yearly conference focusing on the applications and applied aspects of category theory.

Mailing lists

Most of the communication for research and development is usually through (somewhat archaic) mailing lists. Among many, two mailing lists contain the most volume for categorical subjects:

• [categories], a mailing list solely focused on publishing workshops/conferences related to category theory,
• [ALGTOP-L], a mailing list for algebraic topology which sometimes contains content related to category theory.