On (co)ends in ∞\infty-categories

preprint2021arXivOpen access

Abstract

In this short note we prove that two definitions of (co)ends in ∞\infty-categories, via twisted arrow ∞\infty-categories and via ∞\infty-categories of simplices, are equivalent. We also show that weighted (co)limits, which can be defined as certain (co)ends, can alternatively be described as (co)limits over left and right fibrations, respectively.

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