Partial abelian monoids

The topic of this talk is the category of partial abelian monoids: based topological spaces with a partially defined addition. On a large subcategory, we define a tensor product of partial abelian monoids which is universal with respect to certain bilinear maps. This tensor product generalizes at the same time the tensor product of Z-modules and the smash product of based spaces, and gives concise descriptions of several well-known constructions in topology and algebra.