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On the straightening of every functor

2024/08/29 by Blom, Thomas
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.16539

Abstract

We show that any functor between ∞-categories can be straightened. More precisely, we show that for any ∞-category C, there is an equivalence between the ∞-category (Cat)/C of ∞-categories over C and the ∞-category of unital lax functors from C to the double ∞-category Corr of correspondences. The proof relies on a certain universal property of the Morita category which is of independent interest.

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