The monoidal structure of strictification

TL;DR

This paper investigates the monoidal properties of the strictification functor from bicategories to 2-categories, constructing compatible monoidal structures on related 2-categories to deepen understanding of their algebraic framework.

Contribution

It introduces monoidal structures on categories of bicategories and 2-categories, elucidating the monoidal nature of the strictification process.

Findings

Constructed monoidal structures on bicategory and 2-category categories.

Analyzed the monoidal properties of the strictification functor.

Provided a framework for understanding strictification in monoidal contexts.

Abstract

We study the monoidal structure of the standard strictification functor $\textrm{st}:\mathbf{Bicat} \rightarrow \mathbf{2Cat}$. In doing so, we construct monoidal structures on the 2-category whose objects are bicategories and on the 2-category whose objects are 2-categories.