  The aim is the theorems of the title and the corollary that the tensor
product of two free crossed resolutions of groups or groupoids is also a free
crossed resolution of the product group or groupoid. The route to this
corollary is through the equivalence of the category of crossed complexes with
that of cubical omega-groupoids with connections where the initial definition
of the tensor product lies. It is also in the latter category that we are able
to apply techniques of dense subcategories to identify the tensor product of
covering morphisms as a covering morphism.
