On the Barr exactness property of $\mathsf{BXMod/R}$

TL;DR

This paper proves that the category of braided crossed modules over a fixed commutative algebra R is an exact category in the sense of Barr, providing a categorical foundation for these algebraic structures.

Contribution

It establishes the Barr exactness property for the category of braided crossed modules over a fixed commutative algebra R, a foundational result in categorical algebra.

Findings

The category of braided crossed modules over R is Barr exact.

This exactness property facilitates further algebraic and categorical analysis.

The work provides a basis for future research in algebraic structures related to R.

Abstract

In this work, it is shown that the category $\mathsf{BXMod/R}$ of braided crossed modules over a fixed commutative algebra $R$ is an exact category in the sense of Barr.