Peirce allegories. Identities involving transitive elements and symmetrical ones Original Research Article

Peirce allegories are defined. They mix two dual allegory structures, as fuzzy matrix theory does. Sequential applications of the transitive closure, the transitive interior, the symmetric closure and the symmetric interior are studied in Peirce allegories. Semi-direct product of Peirce algebras by finite acting groups are defined. Internal characterization of such algebras is established. Properties of the coimage functor are given. Conversely, a Peirce semi-allegory is associated to a functor (on a suitable category) which resembles a coimage functor.