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arXiv · 2101.08727

On 2-final 2-functors

Jun Maillard
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Abstract

We present a criterion for $2$-final $(2,1)$-functors, analoguous to the classical one for final $1$-functor: a $(2,1)$-functor $F \colon A \to B$ is $2$-final if and only if, for any object $b$ of $B$, the slice $(2,1)$-category $b / F$ is nonempty, connected and simply connected. We also give a combinatorial presentation of paths and homotopies of paths in a $(2,1)$-category.

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Jun Maillard. 2021-01-21. On 2-final 2-functors. https://arxiv.org/abs/2101.08727

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