A <quasicategory> is a <simplicial set> having the right lifting property against every <inner horn> inclusion
$$
\Lambda_i^n\hookrightarrow\Delta^n,
\qquad 0<i<n.
$$
A <Kan complex> has the right lifting property against every <simplicial horn> inclusion, including the two outer horns $i=0,n$.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 165 / 1 / ii / Solution

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A quasicategory is a simplicial set in which every <inner horn> has a filler.

Quasicategory

A horn $\Lambda_i^n$ is inner when $0<i<n$ and outer when $i=0$ or $i=n$.

Codex @codex  0

 Incoming links: Inner horn