2 citations · 4 across the 14 of their papers we have counts for
17 papers
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 from the Hyland, Johnstone and Pitts tripos-to-topos construction. We invest…
Between Markov and restriction. Two more monads on categories for relations
Cipriano Junior Cioffo, Fabio Gadducci, Davide Trotta
The study of categories abstracting the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. In a previou…
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…
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…
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…
On categorical structures arising from implicative algebras: from topology to assemblies
Samuele Maschio, Davide Trotta
Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (bo…
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…
Specification and verification of a linear-time logic for graph transformation
Fabio Gadducci, Andrea Laretto, Davide Trotta
We present a first-order linear-time temporal logic for reasoning about the evolution of directed graphs. Its semantics is based on the counterpart paradigm, thus allowing our logi…
Weakly Markov categories and weakly affine monads
Tobias Fritz, Fabio Gadducci, Paolo Perrone +1
Introduced in the 1990s in the context of the algebraic approach to graph rewriting, gs-monoidal categories are symmetric monoidal categories where each object is equipped with the…
From Gs-monoidal to Oplax Cartesian Categories: Constructions and Functorial Completeness
Tobias Fritz, Fabio Gadducci, Davide Trotta +1
Originally introduced in the context of the algebraic approach to term graph rewriting, the notion of gs-monoidal category has surfaced a few times under different monikers in the…
Generalized existential completions and their regular and exact completions
Maria Emilia Maietti, Davide Trotta
This paper aims to apply the tool of generalized existential completions of conjunctive doctrines, concerning a class of morphisms of their base category, to deepen the study o…
A Presheaf Semantics for Quantified Temporal Logics
Fabio Gadducci, Davide Trotta
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-…
Dialectica Logical Principles
Davide Trotta, Matteo Spadetto, Valeria de Paiva
Gödel's Dialectica interpretation was designed to obtain a relative consistency proof for Heyting arithmetic, to be used in conjunction with the double negation interpretation to o…
The existential completion
Davide Trotta
We determine the existential completion of a primary doctrine, and we prove that the 2-monad obtained from it is lax-idempotent, and that the 2-category of existential doctrines is…
An algebraic approach to the completions of elementary doctrines
Davide Trotta
We provide a thorough algebraic analysis of three known completions having a central role in the exact completions of Lawvere's doctrines: the one adding comprehensive diagonals (i…
Quantifier completions, choice principles and applications
Davide Trotta, Matteo Spadetto
We contribute to the knowledge of the quantifier completions and their applications by using the language of doctrines. This algebraic presentation allows us to properly analyse th…
Compositional theories for host-core languages
Davide Trotta, Margherita Zorzi
Linear type theories, of various types and kinds, are of fundamental importance in most programming language research nowadays. In this paper we describe an extension of Benton's L…