Pseudo-functors modelling higher structures

TL;DR

This paper introduces weakly globular n-fold categories, a new higher categorical structure based on iterated internal categories and weak globularity, with pseudo-functors whose strictification yields these structures.

Contribution

It presents a novel higher categorical framework called weakly globular n-fold categories and connects pseudo-functors with their strictification to model these structures.

Findings

Definition of weakly globular n-fold categories

Identification of pseudo-functors leading to these categories

Establishment of strictification process for pseudo-functors

Abstract

We introduce a new higher categorical structure called a weakly globular n-fold category. This structure is based on iterated internal categories and on the notion of weak globularity. We identify a suitable class of pseudo-functors whose strictification produces weakly globular n-fold categories.