Toward a strictification theorem for co-Segal categories

TL;DR

This paper demonstrates that under certain conditions, co-Segal categories in a monoidal model category can be equivalently strictified, simplifying their structure and analysis.

Contribution

It establishes a strictification theorem for co-Segal categories within monoidal model categories, bridging the gap between lax and strict categorical structures.

Findings

Co-Segal categories are equivalent to strict categories under specific conditions.

The strictification process preserves the monoidal structure.

Provides a framework for simplifying complex categorical models.

Abstract

We show that for a monoidal model category $\M=(\ul{M}, \otimes, I)$, certain co-Segal $\M$-categories are equivalent to strict ones.