# Joyal's CatLab HomePage

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Welcome!

**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

This is a wikion mathematics in parallel to the nLab. The site is just being constructed at the moment. In the long term, the wiki should be useful for research and education in mathematics insofar as the subject is treated with tools and notions of category theory. I keep changing my conception of the wiki but I presently think that it should present a full description of categorical mathematics, including proofs.

The purpose of the Catlab is to make polished expositions of mathematics to facilitate learning by students and researchers.

New: the theory of weak factorisation systems

New: the theory of factorisation systems

New: the theory of distributors

New: the natural model structure on $\mathbf{Cat}$

New: the theory of Quillen model structures

I will be working alone in the CatLab for a while, but I hope other people will join eventually. I may occasionally prove a new result or formulate a conjecture. I would like to give the Catlab an initial shape before letting it free. It could eventually function like a journal with an editorial board and contributors.

Revised on October 8, 2018 at 17:12:40 by Richard Williamson