Category of Generalized Modules Over Two Different Rings - Z. Al-Killabi, Tariq; J. Al-Hwaeer, Hassan; A. Al-Butahi, Ali (Al-Nahrain Journal of Science, 2023)
In this paper, a method of enriched category theory to form a closed symmetric monoidal structure on the category of generalized modules CR = (mod R,Ab) have been implemented. Further, a new kind of generalized module category defined on two commutative rings R and S, denoted by CRS = (mod R,mod S) is constructed. Finally, the authors studied a localization on this type of categories, both of them are Grothendieck.