Homotopies of Lie Crossed Module Morphisms

TL;DR

This paper introduces the concept of homotopy between morphisms of Lie crossed modules, establishing a groupoid structure that organizes these morphisms and their homotopies.

Contribution

It defines homotopy for Lie crossed module morphisms and constructs a groupoid structure to organize these morphisms and their homotopies.

Findings

Defined homotopy of Lie crossed module morphisms

Constructed a groupoid structure for these morphisms and homotopies

Provides a framework for understanding morphism equivalences in Lie algebra contexts

Abstract

In this paper we will define notion homotopy of morphisms of crossed modules of Lie algebras. Then we construct a groupoid structure of Lie crossed module morphisms and their homotopies.