5 papers · 1 filter
A taxonomy of categories for relations
Cipriano Junior Cioffo, Fabio Gadducci, Davide Trotta
The study of categories that abstract the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper…
A topos for extended Weihrauch degrees
Samuele Maschio, Davide Trotta
Weihrauch reducibility is a notion of reducibility between computational problems that is useful to calibrate the uniform computational strength of a multivalued function. It compl…
An Algebraic Abstraction of the Localic Sheafification via the Tripos-to-Topos Construction
Maria Emilia Maietti, Davide Trotta
Localic and realizability toposes are two central classes of toposes in categorical logic, both arising through the Hyland-Johnstone-Pitts tripos-to-topos construction. We investig…
Quotients, pure existential completions and arithmetic universes
Maria Emilia Maietti, Davide Trotta
We provide a new description of Joyal's arithmetic universes through a characterization of the exact and regular completions of pure existential completions. We show that the regul…
When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines
Filippo Bonchi, Alessandro Di Giorgio, Davide Trotta
Fo-bicategories are a categorification of Peirce's calculus of relations. Notably, their laws provide a proof system for first-order logic that is both purely equational and comple…