A <r-complete Boolean algebra is a Boolean algebra in which for every sequence of elements a$-, i = l, • • • , there is an element U?an, the countable union of the a», such that aiQU?an for every i, and such that if diQx for every i then U?anQx. The dual operation, countable intersection, can be introduced through complementation, and the distributive law afMJi*'a» = Uf {aC\an) and its dual can...

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We examine two versions of maps between distributive laws as candidates for wellbehaved translations between structural operational semantics, and validate that by using simple coalgebraic arguments. We give some concrete examples of wellbehaved translations that are maps between distributive laws. The modelling of structural operational semantics uses Turi and Plotkin’s categorical models of G...

In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, ...

Distributive laws between monads (triples) were defined by Jon Beck in the 1960s; see [1]. They were generalized to monads in 2-categories and noticed to be monads in a 2-category of monads; see [2]. Mixed distributive laws are comonads in the 2-category of monads [3]; if the comonad has a right adjoint monad, the mate of a mixed distributive law is an ordinary distributive law. Particular case...

in this paper, we firstly show that the $n$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $n$-dual operation. as a dual result, the $n$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

the purpose of this study barriers and challenges to the development of swimming in iran sports university has focuses on mental and physical health between students and academics. thus the existence of justice is essential to increase its quality in this critical environment. this study investigates distributive and interactive justice in athletic departments&apos; countries universities. popu...

We give a categorical perspective on various product rules, including Brzozowski’s product rule ((st)a = sat + o(s)ta) and the familiar rule of calculus ((st)a = sat+ sta). It is already known that these product rules can be represented using distributive laws, e.g. via a suitable quotient of a GSOS law. In this paper, we cast these product rules into a general setting where we have two monads ...

This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to...