String diagrams for $4$-categories and fibrations of mapping $4$-groupoids

TL;DR

This paper develops a string diagram calculus for strict 4-categories and demonstrates that certain restriction functors between mapping spaces are fibrations of strict 4-groupoids, advancing the understanding of higher categorical structures.

Contribution

It introduces a new string diagram calculus for strict 4-categories and proves a fibration property for restriction functors induced by cofinite inclusions.

Findings

String diagram calculus for strict 4-categories

Restriction functors are fibrations of strict 4-groupoids

Advances understanding of higher categorical structures

Abstract

We introduce a string diagram calculus for strict $4$-categories and use it to prove that given a cofinite inclusion of $4$-categorical presentations, the induced restriction functor on mapping spaces to a fixed target strict $4$-category is a fibration of strict $4$-groupoids.