A lax functor from a bicategory of very general nondeterministic concurrent strategies on concurrent games to the bicategory of profunctors is presented. The lax functor provides a fundamental connection between two approaches to generalizations of domain theory to forms of intensional domain theories, one based on game and strategies, and the other on presheaf categories and profunctors. The l...

In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor on the category of sets. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. T...

The purpose of this paper is study the relationship between the categories of fuzzy multialgebras and crisp algebras. In this regards first we briefly study the categories of multialgebras and fuzzy multialgebras and then by using the fundamental relation of multialgebras we construct a functor from category of fuzzy multialgebras to the category of fuzzy algebras and hence. Hence it can be der...

The classical parabolic induction functor is a fundamental tool on the representation theoretic side of Langlands program. In this article, we study its derived version. It was shown by second author that category smooth G $G$ -representations over k $k$ , p $p$ -adic reductive group and field characteristic equivalent to certain differential graded -algebra H • $H_G^\bullet$ whose zeroth cohom...

In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.

We study relations between the Serre dimension defined as growth of entropy functor and global Bridgeland stability conditions due to Ikeda–Qiu. A fundamental inequality infimum dimensions is proved. Moreover, we characterize Gepner type on fractional Calabi–Yau categories via dimension, classify triangulated lower than one with a condition.

The main purpose of this paper is to introduce the concept of (Γ, n)semihypergroups as a generalization of hypergroups, as a generalization of nary hypergroups and obtain an exact covariant functor between the category (Γ, n)-semihypergrous and the category semigroups. Moreover, we introduce and study complete part. Finally, we obtain some new results and some fundamental theorems in this respect.