Crossed modules of bicomplexes

Abstract EN

This paper is devoted to introduce the notion of crossed modules of bicomplexes as a suitable generalization of the notions of crossed modules of complexes and crossed modules of bigroups, and the notion of bicomplexes as a suitable generalization of the notion of complexes.

This is done by embedding the categories of crossed modules of complexes and crossed modules of bigroups in the category of crossed modules of bicomplexes, and the category of complexes in the category of bicomplexes(via isomorphism of categories).

The notion of bichain complex and bichain map had also been introduced in the beginning of this paper.

Finally, two adjoint pair of functors had been given between the category of crossed modules of bicomplexes and the category of bicomplexes