Joyal's CatLab Quasi-categories

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Definition

Comments or suggestions:

Categorical mathematics

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?

Recall that a simplicial set $X$ is called a Kan complex? if every horn? $\Lambda^k[n]\to X$ has a filler $\Delta[n]\to X$ .

We shall say that a horn $\Lambda^k[n]$ is inner if $0 \lt k \lt n$ , otherwise we shall say that is outer.
We shall say that a simplicial set $X$ is a quasi-category if every inner horn $\Lambda^k[n]\to X$ has a filler $\Delta[n]\to X$ .

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Revised on January 30, 2010 at 19:37:43 by joyal