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 ...

For a compact Hausdorff abelian group K and its subgroup H ≤ K, one defines the g-closure g K (H) of H in K as the subgroup consisting of χ ∈ K such that χ(a n) −→ 0 in T = R/Z for every sequence {a n } inˆK (the Pontryagin dual of K) that converges to 0 in the topology that H induces onˆK. We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive...

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...

Takeuchi’s famous free Hopf algebra construction is analyzed from a categorical point of view, and so is the construction of the Hopf envelope of a bialgebra. Both constructions this way appear as compositions of well known and natural constructions. This way certain partially wrong perceptions of these constructions are clarified and their mutual relation is made precise. The construction of H...

We obtain several Banach-Stone type theorems for vector-valued functions in this paper. Let X,Y be realcompact or metric spaces, E,F locally convex spaces, and φ a bijective linear map from C(X,E) onto C(Y, F ). If φ preserves zero set containments, i.e., z(f) ⊆ z(g)⇐⇒ z(φ(f)) ⊆ z(φ(g)), ∀ f, g ∈ C(X,E), then X is homeomorphic to Y , and φ is a weighted composition operator. The above conclusio...

One of the fundamental problem in rings continuous function is to extract those spaces for which C(X) determines X, that investigate X and Y such isomorphic with C(Y ) implies homeomorphic Y. The development started back from Tychonoff who first pointed out inevitability space this category problem. Later S. Banach M. Stone proved independently slight variance, if compact Hausdorff space, also ...

Several attempts have been made of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets, 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 expressed as a coreflection between the category of (semi-weighted) graph grammars a...