Tensor product of partially-additive monoids
Partially-additive monoids (pams) were introduced by Arbib and Manes in order to provide an algebraic semantics for programming languages. In this paper, we prove that the category \({\mathcal P}am\) of pams and additive maps is a closed category whose monoids are partially-additive semirings. We follow the tensor product construction of \textit{R. Guitart} [Cah. Topologie Géom. Différ. 21, 5-62 (1980; Zbl 0477.18007)] for categories of algebras which generalize the case of modules. Nevertheless, the problem here is more difficult owing to the fact that pams are partial algebras rather than algebras. Thus, we have to make some modifications to Guitart's approach.
scientific article; zbMATH DE number 3899133