Descent for internal multicategory functors

TL;DR

This paper establishes conditions for effective descent in categories of internal multicategories, using equalizer constructions and extending descent techniques for algebraic structures.

Contribution

It introduces two approaches to analyze effective descent morphisms in internal multicategory categories, expanding existing theoretical frameworks.

Findings

Effective descent conditions are characterized for internal multicategories.

Two methods are developed: equalizer-based and extension of algebraic descent techniques.

Results facilitate understanding of morphism behavior in complex categorical structures.

Abstract

We give sufficient conditions for effective descent in categories of (generalized) internal multicategories. Two approaches to study effective descent morphisms are pursued. The first one relies on establishing the category of internal multicategories as an equalizer of categories of diagrams. The second approach extends the techniques developed by Ivan Le Creurer in his study of descent for internal essentially algebraic structures.