Stochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of real-world systems. It enables realistic performance modeling, quality-of-service guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus have emerged as effective tools to describe and reason about systems exhibiting stochastic behavior...

We introduce update monads as a generalization of state monads. Update monads are thecompatible compositions of reader and writer monads given by a set and a monoid. Distributivelaws between such monads are given by actions of the monoid on the set.We also discuss a dependently typed generalization of update monads. Unlike simple updatemonads, they cannot be factored into a ...

Abstract It is well known that classical varieties of $\Sigma$ -algebras correspond bijectively to finitary monads on $\mathsf{Set}$ . We present an analogous result for ordered -algebras, is, categories algebras presented by inequations between -terms. prove they strongly $\mathsf{Pos}$ That those which preserve reflexive coinserters. deduce have a coinserter presentation, the coequalizer pres...

In this paper, we give a novel abstract description of Szabo’s polycategories. We use the theory of double clubs – a generalisation of Kelly’s theory of clubs to ‘pseudo’ (or ‘weak’) double categories – to construct a pseudo-distributive law of the free symmetric strict monoidal category pseudocomonad onMod over itself qua pseudomonad, and show that monads in the ‘two-sided Kleisli bicategory’ ...

A new categorical framework is provided for dealing with multiple arguments in a programming language with effects, for example in a language with imperative features. Like related frameworks (Monads,Arrows, Freyd categories), we distinguish two kinds of functions. In addition, we also distinguish two kinds of equations. Then, we are able to define a kind of product, that generalizes the usual ...

It it shown that geometric morphisms between elementary toposes can be represented as adjunctions between the corresponding categories of locales. These adjunctions are characterised as those that preserve the order enrichment, commute with the double power locale monad and whose right adjoints preserve finite coproduct. They are also characterised as those adjunctions that preserve the order e...

We introduce a general categorical framework for the definition of weak behavioural equivalences, building on and extending recent results in the field. This framework is based on special order enriched categories, i.e. categories whose homsets are endowed with suitable complete orders. Using this structure we provide an abstract notion of saturation, which allows us to define various (weak) be...