The free distributive completion of a partial complete lattice is the complete lattice that it is freely generated by the partial complete latticèin the most distributive way'. This can be described as being a universal solution in the sense of universal algebra. Free distributive completions generalize the constructions of tensor products and of free completely distributive complete lattices o...

This thesis presents a series of theoretical results and practical realisations about the theory of computation in distributive categories. Distributive categories have been proposed as a foundational tool for Computer Science in the last years, starting from the papers of R.F.C. Walters. We shall focus on two major topics: distributive computability, i.e., a generalized theory of computability...

A category with finite products and finite coproducts is said to be distributive if the canonical map A×B + A×C → A× (B + C) is invertible for all objects A, B, and C. Given a distributive category D , we describe a universal functor D → Dex preserving finite products and finite coproducts, for which Dex is extensive; that is, for all objects A and B the functor Dex/A × Dex/B → Dex/(A + B) is a...

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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...