# Joyal's CatLab Quasi-categories

Definition

Comments or suggestions:

Categorical mathematics

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

### Definition

• 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