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Collaboratively edited wiki written by working mathematicians, covering category theory, higher categories, and mathematical physics from an nPOV. Entries are dense and heavily cross-referenced, useful for chasing definitions and connections once basic vocabulary is already in place.
More resources on Categories
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Kerodon
An open, continuously updated online reference for homotopy-coherent mathematics, covering simplicial sets, Kan complexes, and infinity-categories chapter by chapter with tagged, cross-linked proofs readers can cite and follow from foundations through higher category theory.
Category Theory for Programmers
Bartosz Milewski's blog series translating categorical ideas into Haskell and C++ terms, with a free companion book. Readers finish able to reason about functors, natural transformations, and monads as everyday programming abstractions rather than abstract algebra.
Category Theory for Programmers
Learn category theory fundamentals with Bartosz Milewski's engaging course for programmers. Master categories and their applications!
Category Theory
Oxford Logic Guides text building category theory from scratch for readers with some logic or algebra background. Working through the exercises gives command of limits, adjoints, monads, and the categorical treatment of propositional and higher-order logic.
Categories for the Working Mathematician
The standard graduate reference by one of the field's founders, assuming comfort with algebra and topology. Covers limits, adjoints, monads, Kan extensions, and monoidal categories, and remains the source most later texts and papers cite.