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

Davide di Micco and Tim Van der Linden

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.

Keywords: Semi-abelian category, pair of compatible actions, internal action, crossed module, crossed square, commutator, non-abelian tensor product

2020 MSC: 18D40, 18E13, 20J15

Theory and Applications of Categories, Vol. 35, 2020, No. 34, pp 1268-1311.

Published 2020-07-31.

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