In 2010, J. Climent Vidal and J. Soliveres Tur developed, among other things, a pair of 2-adjunctions between the 2-category of adjunctions and the 2-category of monads. One is related to the Kleisli adjunction and the other to the Eilenberg-Moore adjunction for a given monad.Since any 2-adjunction induces certain natural isomorphisms of categories, these can be used to classify bijection...

In the present paper, by considering the notion of ideals in $MV$-algebras, we study some kinds of ideals in $MV$-algebras and obtain some results on them. For example, we present definition of ultra ideal in $MV$-algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$...

We determine the regular representations, Gabriel quivers and representation type of all liftings of two-dimensional quantum linear spaces

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

Multirelations provide a semantic domain for computing systems that involve two dual kinds of nondeterminism. This paper presents relational formalisations of Kleisli, Parikh and Peleg compositions and liftings of multirelations. These liftings are similar to those that arise in the Kleisli category of the powerset monad. We show that Kleisli composition of multirelations is associative, but ne...

In control related studies, convex liftings have been of use to solve inverse parametric linear/quadratic programming problem. This paper presents a so-called convex liftings based method for robust control design of constrained linear systems affected by bounded additive disturbances. It will be shown that a geometrical construction as convex lifting can be used in optimization-based control d...

There exist two different generalizations of the classical Saito–Kurokawa lifting to modular forms with (square-free) level; one lifting produces modular forms with respect to Γ0(m), the other one with respect to the paramodular group Γ(m). We shall give an alternative and unified construction of both liftings using group theoretic methods. The construction shows that a single elliptic modular ...