Weakly globular N-fold categories as a model of weak N-categories

TL;DR

This paper introduces weakly globular n-fold categories as a new model for weak n-categories, demonstrating their equivalence to existing models and their application to algebraic models of n-types.

Contribution

It establishes weakly globular n-fold categories as a valid model for weak n-categories and connects them to algebraic models of n-types.

Findings

Proves equivalence to Tamsamani-Simpson model

Introduces groupoidal weakly globular n-fold categories

Shows they model n-types algebraically

Abstract

We study a new type of higher categorical structure, called weakly globular n-fold category, previously introduced by the author. We show that this structure is a model of weak n-categories by proving that it is suitably equivalent to the Tamsamani-Simpson model. We also introduce groupoidal weakly globular n-fold categories and show that they are algebraic models of n-types.