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The menagerie of epimorphisms in the category Cat of small categories is studied. The standard notion of a congruence on a category is generalized and used subsequently to introduce the notion of a kernel of a functor, quotient category and quotient functor. Theory of concurrent processes seems to be a natural place to look for applications of the notions and results presented here in the area of...
A new notion of a general morphism of Petri nets is introduced. The new morphisms are shown to properly include the morphisms considered so far. The resulting category of general Petri nets is shown to admit products. Here, it is shown that the new notion turns out to be indispensable to facilitate functoriality of synthesis of transition systems by means of (labelled) state machines. In the companion...
Omawiany jest problem znajdowania (funktorialnej) współbieżnej realizacji systemu reaktywnego jako etykietowanej bezpiecznej sieci Petriego. Najpierw opisana jest funktorialna konstrukcja prowadząca z kategorii konkretnych systemów asynchronicznych, wprowadzonych przez Morina, do kategorii etykietowanych bezpiecznych sieci Petriego. Następnie omówiony jest problem w pełnej ogólności. Na ogół nie istnieje...
We study the problem of embedding partial 2-structures into set 2-structures such that the target substructure is full and forward closed and it is minimal w.r.t. these properties.
The paper is concerned with algebras whose elements can be used to represent runs of a system from a state to a state. These algebras, called multiplicative transition systems, are categories with respect to a partial binary operation called composition. They can be characterized by axioms such that their elements and operations can be represented by partially ordered multisets of a certain type and...
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