A Fubini rule for $\infty$-coends

TL;DR

This paper establishes a Fubini rule for $ abla$-co/ends of $ abla$-functors in $ abla$-categories, enabling integration-like rules in the realm of $ abla$-categories, extending classical calculus concepts.

Contribution

It introduces a Fubini rule for $ abla$-co/ends of $ abla$-functors, generalizing classical co/end calculus to $ abla$-categories.

Findings

Provides a formal Fubini rule for $ abla$-co/ends

Enables 'integration rules' in $ abla$-category setting

Extends classical calculus concepts to higher categories

Abstract

We prove a Fubini rule for $\infty$-co/ends of $\infty$-functors $F : \mathcal C^\text{op}\times\mathcal C\to \mathcal D$. This allows to lay down "integration rules", similar to those in classical co/end calculus, also in the setting of $\infty$-categories.