Bicategories and Weakly Globular Double Categories

TL;DR

This paper introduces weakly globular double categories as a new strict double category class to model weak 2-categories, constructs a double category of fractions, and demonstrates their use in algebraic homotopy 2-type modeling.

Contribution

It defines weakly globular double categories, develops a double category of fractions, and shows their application as an algebraic model for homotopy 2-types.

Findings

Weakly globular double categories effectively model weak 2-categories.

A double category of fractions is constructed within this framework.

The sub-2-category of groupoidal weakly globular double categories models homotopy 2-types.

Abstract

This paper introduces the notion of weakly globular double categories, a particular class of strict double categories, as a way to model weak 2-categories; it explores its use in defining a double category of fractions, and shows that the sub-2-category of groupoidal weakly globular double categories forms an algebraic model of homotopy 2-types.