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Stream: theory: category theory

Topic: final (n, 1)-functors

Jun Maillard (Dec 28 2020 at 15:59):

Hello,
There is criterion for final functors: a functor $F \colon A \to B$ is final if and only if, for any object $b \in B$, the slice category $b / F$ is nonempty and connected. A criterion also exists for $(\infty,1)$-categories: an $(\infty, 1)$-functor $A \to B$ is $\infty$-final if and only if for any object $b \in B$, the slice $\infty$-category $b / F$ is weakly contractible.

I am looking for a reference of a similar criterion (in particular for n = 2) for a "n-final" (n,1)-functors $F \colon A \to B$: for any object $b \in B$, $\pi_k(b / F)$ is trivial for $0 \leq k \leq n$.