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Transition system theory arises in several branches of mathematics including algebraic automata theory and universal algebra theory. In this paper, some key questions related to the notions of retraction and injectivity are answered in the category of transition systems over a given alphabet. This yields results concerning the parallel decomposition problem of a transition system.
The notions of retraction and injectivity have been useful in the study of many categories (category of modules over a ring, category of posets, category of metric spaces over an Heyting albegra ...).In this article the category of Σ-transition algebras is considered, and in this frame, answers are given to the key questions related to these notions. For instance it is shown:-how to construct all...
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