Related papers: A Categorical Semantics for Guarded Petri Nets
The Grothendieck construction is a process to form a single category from a diagram of small categories. In this paper, we extend the definition of the Grothendieck construction to diagrams of small categories enriched over a symmetric…
Modelling, specifying and reasoning about complex systems requires to process in an integrated fashion declarative and procedural aspects of the target domain. The paper reports on an experiment conducted with a propositional version of…
We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids.…
Gene regulatory network (GRN) plays a central role in system biology and genomics. It provides a promising way to model and study complex biological processes. Several computational methods have been developed for the construction and…
In this article, we characterize convexity in terms of algebras over a PROP, and establish a tensor-product-like symmetric monoidal structure on the category of convex sets. Using these two structures, and the theory of $\scr{O}$-monoidal…
We investigate the decidability of termination, reachability, coverability and deadlock-freeness of Petri nets endowed with a hierarchy on places, and with inhibitor arcs, reset arcs and transfer arcs that respect this hierarchy. We also…
In this document, we collect a list of categorical structures on the category $\mathbf{Poly}$ of polynomial functors. There is no implied claim that this list is in any way complete. It includes: infinitely many monoidal structures, all but…
The role of types in categorical models of meaning is investigated. A general scheme for how typed models of meaning may be used to compare sentences, regardless of their grammatical structure is described, and a toy example is used as an…
This paper contains introductory material on Petri nets and Groebner basis theory and makes some observations on the relation between the two areas. The aim of the paper is to show how Groebner basis procedures can be applied to the problem…
Categorical structures and their pseudomaps rarely form locally presentable 2-categories in the sense of Cat-enriched category theory. However, we show that if the categorical structure in question is sufficiently weak (such as the…
Causal nets (CNs) are Petri nets where causal dependencies are modelled via inhibitor arcs. They play the role of occurrence nets when representing the behaviour of a concurrent and distributed system, even when reversibility is considered.…
Step net bisimilarity \cite{Gor23} is a truly concurrent behavioral equivalence for finite Petri nets, which is defined as a smooth generalization of standard step bisimilarity \cite{NT84} on Petri nets, but with the property of relating…
In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors…
Petri nets are a mathematical language for modeling and reasoning about distributed systems. In this paper we propose an approach to Petri nets for embedding reversibility, i.e., the ability of reversing an executed sequence of operations…
When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning,…
Recently, there has been renewed interest in the theory and applications of de Paiva's dialectica categories and their relationship to the category of polynomial functors. Both fall under the theory of generalized polynomial categories,…
It has long been known that every weak monoidal category A is equivalent via monoidal functors and monoidal natural transformations to a strict monoidal category st(A). We generalise the definition of weak monoidal category to give a…
The study of categories that abstract the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper strives to provide a modern presentation of these…
We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor…
The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.