Internal bicategories in groups

TL;DR

This paper explores the structure of internal bicategories within the category of groups, deriving from general theories and providing specific examples like the bicategory of paths in topological abelian groups.

Contribution

It extends the theory of internal bicategories to groups and related categories, including explicit examples and descriptions in weakly Mal'tsev categories.

Findings

Derived a detailed description of internal bicategories in groups.

Presented an example of bicategory of paths in a topological abelian group.

Described internal bicategories in weakly Mal'tsev categories with V-Mal'tsev operations.

Abstract

A detailed description of internal bicategory in the category of groups is derived from the general description of internal bicategories in weakly Mal'tsev sesquicategories. The example of bicategory of paths in a topological abelian group is presented, as well as a description of internal bicategories in weakly Mal'tsev categories with a $V$-Mal'tsev operation in the sense of Pedicchio.