Rétractions, corétractions et enveloppe injective d'une algèbre de transitions

AbstractThe 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 the retraction types of a given Σ-transition algebra.—that the category of Σ-transition algebras has enough injective objects and an injective cogenerator.—that every Σ-transition algebras has an injective envelope.These allow to obtain results concerning the structure and the decomposition of a Σ-transition algebra