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Riguet and Generalized Congruences on a Category: Relationships and Applications
Juan Climent Vidal, Enric Cosme Llópez, Raúl Ruiz Mora
We investigate Riguet congruences and generalized congruences on a category, focusing on their interrelations from both lattice-theoretic and category-theoretic perspectives. We al…
From higher-order rewriting systems to higher-order categorial algebras and higher-order Curry-Howard isomorphisms
Juan Climent Vidal, Enric Cosme Llópez, Raúl Ruiz Mora
This ongoing project aims to define and investigate, from the standpoint of category theory, order theory and universal algebra, the notions of higher-order many-sorted rewriting s…
Lallement functor is a weak right multiadjoint
Juan Climent Vidal, Enric Cosme Llópez
For a plural signature and with regard to the category , of naturally preordered idempotent -algebras and surjective homomorphisms, we defin…
Płonka Adjunction
Juan Climent Vidal, Enric Cosme Llópez
For a signature and its subsignature without -ary operation symbols, we prove (1) that there are strong Lawvere adjoint cylinders between the category $\mathsf{…
When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?
Juan Climent Vidal, Enric Cosme Llópez
For a set of sorts and an -sorted signature we prove that a profinite -algebra, i.e., a projective limit of a projective system of finite -algebras, is a retract o…
On the Morphisms and Transformations of Tsuyoshi Fujiwara (as a concretion of a bidimensional many-sorted general algebra and its application to the equivalence between many-sorted clones and algebraic theories)
Juan Climent Vidal, Juan Soliveres Tur
For single-sorted algebras, Fujiwara defined, through the concept of family of basic mapping-formulas, a notion of morphism which generalizes the ordinary notion of homomorphism be…