More on crossed modules of Lie, Leibniz, associative and diassociative algebras

TL;DR

This paper explores the relationships between crossed modules of various algebraic structures, extending known category relations to include dialgebras and Leibniz algebras, and constructs adjoint functors between these categories.

Contribution

It introduces adjoint functors between categories of crossed modules of dialgebras and Leibniz algebras, extending classical relations to these categories.

Findings

Construction of adjoint functors between categories

Extension of relations from classical algebras to crossed modules

Enhanced understanding of algebraic category relationships

Abstract

Adjoint functors between the categories of crossed modules of dialgebras and Leibniz algebras are constructed. The well-known relations between the categories of Lie, Leibniz, associative algebras and dialgebras are extended to the respective categories of crossed modules.