An intrinsic approach to the non-abelian tensor product via internal crossed squares

TL;DR

This paper introduces an intrinsic method for constructing the non-abelian tensor product within semi-abelian categories using internal crossed squares, providing a new categorical perspective.

Contribution

It develops an intrinsic categorical framework for the non-abelian tensor product via internal crossed squares in semi-abelian categories, advancing theoretical understanding.

Findings

Establishes a new categorical approach to non-abelian tensor products.

Connects internal crossed squares with the Brown-Loday tensor product.

Provides foundational results for further categorical studies.

Abstract

We explain how, in the context of a semi-abelian category, the concept of an internal crossed square may be used to set up an intrinsic approach to the Brown-Loday non-abelian tensor product.