5 citations · 13 across the 11 of their papers we have counts for
12 papers
Difference-restriction algebras with operators
Célia Borlido, Ganna Kudryavtseva, Brett McLean
We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff étale spaces. Differe…
Filtral pretoposes and compact Hausdorff locales
Célia Borlido, Panagis Karazeris, Luca Reggio +1
The category of compact Hausdorff locales is a pretopos which is filtral, meaning that every object is covered by one whose subobject lattice is isomorphic to the lattice of filter…
Pervin spaces and Frith frames: bitopological aspects and completion
Célia Borlido, Anna Laura Suarez
A Pervin space is a set equipped with a bounded sublattice of its powerset, while its pointfree version, called Frith frame, consists of a frame equipped with a generating bounded…
A pointfree theory of Pervin spaces
Célia Borlido, Anna Laura Suarez
We lay down the foundations for a pointfree theory of Pervin spaces. A Pervin space is a set equipped with a bounded sublattice of its powerset, and it is known that these objects…
Substitution Principle and semidirect products
Célia Borlido, Mai Gehrke
In the classical theory of regular languages the concept of recognition by profinite monoids is an important tool. Beyond regularity, Boolean spaces with internal monoids (BiMs) we…
Difference-restriction algebras of partial functions with operators: discrete duality and completion
Célia Borlido, Brett McLean
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a col…
Difference-restriction algebras of partial functions: axiomatisations and representations
Célia Borlido, Brett McLean
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide…
Difference hierarchies and duality with an application to formal languages
Célia Borlido, Mai Gehrke, Andreas Krebs +1
The notion of a difference hierarchy, first introduced by Hausdorff, plays an important role in many areas of mathematics, logic and theoretical computer science such as descriptiv…
A note on powers of Boolean spaces with internal semigroups
Célia Borlido, Mai Gehrke
Boolean spaces with internal semigroups generalize profinite semigroups and are pertinent for the recognition of not-necessarily regular languages. Via recognition, the study of ex…
Complete kappa-reducibility of pseudovarieties of the form DRH
Jorge Almeida, Célia Borlido
We denote by kappa the implicit signature that contains the multiplication and the (omega-1)-power. It is proved that for any completely kappa-reducible pseudovariety of groups H,…
The kappa-word problem over DRH
Célia Borlido
Let H be a pseudovariety of groups in which the kappa-word problem is decidable. Here, kappa denotes the canonical implicit signature, which consists of the multiplication and the…
Some reducibility properties for pseudovarieties of the form DRH
Célia Borlido
Let H be a pseudovariety of groups and DRH be the pseudovariety containing all finite semigroups whose regular R-classes belong to H. We study the relationship between reducibility…