We use the theta correspondence to study the equivalence between Godement-Jacquet and Jacquet-Langlands L-functions for. We show that the resulting comparison is in fact an expression of an exotic symmetric monoidal structure on the category of -modules. Moreover, this enables us to construct an abelian category of abstractly automorphic representations, whose irreducible objects are the usual automorphic representations. We speculate that this category is a natural setting for the study of automorphic phenomena for, and demonstrate its basic properties. This paper is a part of the author's thesis .