Interchange of filtered 2-colimits and finite 2-limits

TL;DR

This paper investigates the interaction between filtered 2-colimits and finite 2-limits within the 2-category of small categories, generalizing a classical category theory result.

Contribution

It proves that filtered 2-colimits commute with finite 2-limits in CAT, extending known classical theorems to 2-categorical context.

Findings

Filtered 2-colimits and finite 2-limits commute in CAT

Generalization of classical category theory result

Enhances understanding of 2-categorical limits and colimits

Abstract

In this paper we go into the study of 2-limits and 2-colimits in the 2-category CAT the category of small categories. More precisely we show the commutation of filtered 2-colimits and finite 2-limits. It is a generalization of a classical result in category theory.