semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.

Compactifications of biframes are defined, and characterized internally by means of strong inclusions. The existing description of the compact, zero-dimensional coreflection of a biframe is used to characterize all zero-dimensional compactifications, and a criterion identifying them by their strong inclusions is given. In contrast to the above, two sufficient conditions and several examples sho...

Semi-regular locales are extensions of the classical semiregular spaces. We investigate the conditions such that semi-regularization is a functor. We also investigate the conditions such that semi-regularization is a reflection or coreflection.

The problem of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets has been faced several times along the years, both for the single-pushout and double-pushout approaches, but only partial results were obtained. In this paper we fully extend Winskel’s approach to single-pushout grammars providing them with a categorical concurrent semantics ...

Petri Place/Transition (PT) nets are one of the most widely used models of concurrency. However, they still lack, in our view, a satisfactory semantics: on the one hand the “token game” is too intensional, even in its more abstract interpretations in term of nonsequential processes and monoidal categories; on the other hand, Winskel’s basic unfolding construction, which provides a coreflection ...

We introduce the notion of strongly concatenable process as a refinement of concatenable processes [3] which can be expressed axiomatically via a functor Q[ ] from the category of Petri nets to an appropriate category of symmetric strict monoidal categories, in the precise sense that, for each net N , the strongly concatenable processes of N are isomorphic to the arrows of Q[N ]. In addition, w...

Local event structures and local traces are generalizations of the classical prime event structures and Mazurkiewicz’ traces in which independence is no longer a global binary property. We consider the problem of lifting the categorical connection between prime event structures and Mazurkiewicz’ traces to this more general setting. Using a generic approach it is shown how certain subcategories ...

We introduce a generalisation of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed λ-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions...

We introduce the notion of strongly concatenable process as a refinement of concatenable processes (Degano et al. 1996) which can be expressed axiomatically via a functor Q ( ) from the category of Petri nets to an appropriate category of symmetric strict monoidal categories, in the precise sense that, for each net N, the strongly concatenable processes of N are isomorphic to the arrows of Q (N...