Abstract. Many kinds of morphisms on Petri nets have been defined and studied. They can be used as formal techniques supporting refinement/abstraction of models. In this paper we introduce a new notion of morphism on marked graphs, a class of Petri nets used for the representation of systems having deterministic behavior. Such morphisms can indeed be used to represent a form of abstraction on m...

We explore connections between places of function fields over a base field F and birational morphisms between smooth F varieties. This is done by considering various categories of fractions involving function fields or varieties as objects, and constructing functors between these categories. The main result is that in the localised category S b Sm(F ), where Sm(F ) denotes the usual category of...

Concurrent separation logic is distinguished by transfer of state ownership upon parallel composition and framing. The algebraic structure that underpins partial commutative monoids (PCMs). Extant research considers primarily from the logical perspective while comparatively less attention drawn to considerations. This paper provides an formalization in concurrent means structure-preserving func...

Nick Gurski’s new book addresses some central concerns of the subject known as higher category theory; and yet, it is some distance from what many people now understand by that term. This may puzzle some. I will therefore begin by locating Gurski’s book within the mathematical landscape. Let n ∈ N ∪ {∞}. Roughly, an n-category consists of some objects, some 1-morphisms between objects, some 2-m...

~ e semantic domain for object-oriented languages and systems outlined in this paper is an amalgamation of two approaches: the objects-as-sheaves approach of the second author published nearly two decades ago, and the more recent ideas of the first and third authors on objects as processes endowed with observation. The basic insight is that objects in the latter sense correspond to object morph...

A morphism h is called ambiguous for a string s if there is another morphism that maps s to the same image as h; otherwise, it is called unambiguous. In this paper, we examine some fundamental problems on the ambiguity of erasing morphisms. We provide a detailed analysis of so-called ambiguity partitions, and our main result uses this concept to characterise those strings that have a morphism o...

An infinite word, which is aperiodic and codes the orbit of a transformation of the exchange of three intervals is called 3iet word. Such a word is thus a natural generalization of a sturmian word to a word over 3-letter alphabet. A morphism is said to be 3iet preserving if it maps any 3iet word to another 3iet word. It is known that the monoid of morphisms preserving sturmian words is finitely...