(1) c/o G. Cedraschi, 1 Rue des Minoteries, Geneva, 1205, Switzerland
Abstract:
The projective tensor product in a category of topological R-modules (where R is a topological ring) can be defined in Top, the category of topological spaces, by the same universal property used to define the tensor product of R-modules in Set. In this article, we extend this definition to an arbitrary topological category X and study how the Cartesian closedness of X is related to the monoidal closedness of the category of R-module objects in X.
Mathematics Subject Classifications (2000) 18D15, 18D35, 18A40.