On (co)ends in $\infty$-categories

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.

arXiv comment14 pages, v2: Added two further descriptions of coends

References in corpus (2)

• Shifted Coisotropic Correspondences
• A Fubini rule for $\infty$-coends

Cited by in corpus (2)

• Fibrations and lax limits of $(\infty ,2)$-categories
• Real K-theory for Waldhausen infinity categories with genuine duality