Tensor products of categories of equivariant perverse sheaves
In this paper the notion of a ternary semigroup of morphisms of objects in a category is introduced. The connection between an isomorphism of categories and an isomorphism of ternary semigroups of morphisms of suitable objects in these categories is considered. Finally, the results obtained for general categories are applied to the categories and which were studied in [5].
Quantum integrals associated to quantum Hom-Yetter-Drinfel’d modules are defined, and the affineness criterion for quantum Hom-Yetter-Drinfel’d modules is proved in the following form. Let (H,α) be a monoidal Hom-Hopf algebra, (A,β) an (H,α)-Hom-bicomodule algebra and . Under the assumption that there exists a total quantum integral γ: H → Hom(H,A) and the canonical map , , is surjective, we prove that the induction functor is an equivalence of categories.
We determine the algebraic groups which have a close relation to the Roth inequalities.