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Peirce allegories. Identities involving transitive elements and symmetrical ones. (English) Zbl 0867.18003

Summary: 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.

MSC:

18B10 Categories of spans/cospans, relations, or partial maps
03G15 Cylindric and polyadic algebras; relation algebras
03E72 Theory of fuzzy sets, etc.
03E20 Other classical set theory (including functions, relations, and set algebra)
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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