Retractions, coretractions et enveloppe injective d'une algebre de transitions

摘要

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 algebra …). In this article the category of ∑-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 ∑-transition algebra. - that the category of ∑-transition algebras has enough injective objects and an injective cogenerator. - that every ∑-transition algebras has an injective envelope. These allow to obtain results concerning the structure and the decomposition of a ∑-transition algebra.