Joyal's CatLab
Basic category theory

Comments or suggestions: I think there should perhaps be a section on ‘new categories from old ones’ or something similar, covering e.g. (co)comma categories, (co)slice categories, functor categories, and product categories. I can start it myself, but I really only know about (co)comma and functor categories. Though I suppose it’s a good reason to learn other constructions.

**Category theory** ##Contents * Contributors * References * Introduction * Basic category theory * Weak factorisation systems * Factorisation systems * Distributors and barrels * Model structures on Cat * Homotopy factorisation systems in Cat * Accessible categories * Locally presentable categories * Algebraic theories and varieties of algebras

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*** **Categorical mathematics** ##Contents * Set theory * Category theory * Homotopical algebra * Higher category theory * Theory of quasi-categories * Higher quasi-categories * Geometry * Elementary geometry * Differential geometry * Lie theory * Algebraic geometry * Homotopical algebraic geometry * Number theory * Elementary number theory * Algebraic number theory * Algebra * Universal algebra * Group theory * Rings and modules * Commutative algebras * Lie algebras * Representation theory * Operads * Homological algebra * Logic * Boolean algebra * First order theory * Model theory * Categorical logic * Topology * General topology * Algebraic topology * Homotopy theory * Theory of locales * Topos theory * Higher topos theory * Combinatorics * Combinatorial geometry * Enumerative combinatorics * Algebraic combinatorics

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Basic Category Theory

Contents

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Revised on September 1, 2012 at 22:46:30 by jstalfos