Tensor Products and Bimorphisms

Abstract

The binary tensor product, for modules over a commutative ring, has two different aspects: its connection with universal bilinear maps and its adjointness to the internal hom-functor. Furthermore, in the special situation of finite-dimensional vector spaces, the tensor product can also be described in terms of dual spaces and the internal hom-functor. The aim of this paper is to investigate these relationships in the setting of arbitrary concrete categories.