Coverings and crossed modules of topological groups with operations

TL;DR

This paper generalizes the classical covering group theory to topological groups with operations, including the construction of covers for crossed modules within this broader class.

Contribution

It extends the theory of covering groups to topological groups with operations and introduces coverings for crossed modules in this context.

Findings

Generalization of covering group theory to topological groups with operations

Construction of covers for crossed modules within these groups

Broader applicability to algebraic structures with topological and operational features

Abstract

It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic group $G$. In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also give the cover of crossed modules within topological groups with operations.