Weakly globular Tamsamani N-categories and their rigidification

TL;DR

This paper introduces weakly globular Tamsamani n-categories, a new higher categorical structure that generalizes existing models using weak globularity, and proves their equivalence to weakly globular n-fold categories.

Contribution

It defines weakly globular Tamsamani n-categories and establishes their equivalence with weakly globular n-fold categories, advancing the theory of higher categories.

Findings

Weakly globular Tamsamani n-categories are introduced.

Proved equivalence with weakly globular n-fold categories.

Generalizes the Tamsamani-Simpson model.

Abstract

We introduce a new class of higher categorical structures called weakly globular Tamsamani n-categories. These generalize the Tamsamani-Simpson model of higher categories by using the new paradigm of weak globularity to weaken higher categorical structures. We prove this new structure is suitably equivalent to a simpler one previously introduced by the author, called weakly globular n-fold categories.