Categorical Results in the Theory of Two-Crossed Modules of Commutative Algebras

TL;DR

This paper investigates categorical properties of 2-crossed modules of commutative algebras, extending previous work, and examines functorial structures and free constructions within this algebraic framework.

Contribution

It extends the categorical theory of 2-crossed modules of commutative algebras and analyzes the fibred and cofibred nature of the forgetful functor, including free module constructions.

Findings

The forgetful functor is fibred and cofibred.

Construction of induced and coinduced 2-crossed modules.

Application of free 2-crossed modules.

Abstract

In this paper we explore some categorical results of 2-crossed module of commutative algebras extending work of Porter in [18]. We also show that the forgetful functor from the category of 2-crossed modules to the category of k-algebras, taking {L, M, P, \partial_2, \partial_1} to the base algebra P, is fibred and cofibred considering the pullback (coinduced) and induced 2-crossed modules constructions, respectively. Also we consider free 2- crossed modules as an application of induced 2-crossed modules.