82 citations · 120 across the 21 of their papers we have counts for
5 papers · 1 filter
Unifying exact completions
Maria Emilia Maietti, Giuseppe Rosolini
We define the notion of exact completion with respect to an existential elementary doctrine. We observe that the forgetful functor from the 2-category exact categories to existenti…
Convergence in Formal Topology: a unifying notion
Francesco Ciraulo, Maria Emilia Maietti, Giovanni Sambin
Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that o…
Elementary quotient completion
Maria Emilia Maietti, Giuseppe Rosolini
We extend the notion of exact completion on a weakly lex category to elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which freely adds…
Constructive version of Boolean algebra
Francesco Ciraulo, Maria Emilia Maietti, Paola Toto
The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: w…
Quotient completion for the foundation of constructive mathematics
Maria Emilia Maietti, Giuseppe Rosolini
We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional t…