Equivalence between the category of Cat¹-complexes and the category of crossed modules of complexes

Abstract EN

In t his paper, we introduce the notion of cat¹-complexes as a suitable generalization of the cat¹- groups through embedding the category of cat¹- groups in the category of Cat¹-complexes as a subcategory (via isomorphism of categories).

It was shown that the category of Cat¹ complexes is equivalent to the category of crossed modules of complexes as well as the couple of two covariant functors used to show the equivalence between these two categories are represent an adjoint pair of functos.