23 citations · 34 across the 7 of their papers we have counts for
9 papers
A comonad for Grothendieck fibrations
Jacopo Emmenegger, Luca Mesiti, Giuseppe Rosolini +1
We prove that cloven Grothendieck fibrations over a fixed base $\ct{B}$ are the pseudo-coalgebras for a lax idempotent 2-comonad on $\ct{Cat}/\ct{B}$. We show this via an original…
Quasitoposes as elementary quotient completions
Maria Emilia Maietti, Fabio Pasquali, Giuseppe Rosolini
The elementary quotient completion of an elementary doctrine in the sense of Lawvere was introduced in previous work by the first and third authors. It generalises the exact comple…
Doctrines, modalities and comonads
Francesco Dagnino, Giuseppe Rosolini
Doctrines are categorical structures very apt to study logics of different nature within a unified environment: the 2-category Dtn of doctrines. Modal interior operators are charac…
A characterisation of elementary fibrations
Jacopo Emmenegger, Fabio Pasquali, Giuseppe Rosolini
Grothendieck fibrations provide a unifying algebraic framework that underlies the treatment of various form of logics, such as first order logic, higher order logics and dependent…
Elementary Quotient Completions, Church's Thesis, and Partioned Assemblies
Maria Emilia Maietti, Fabio Pasquali, Giuseppe Rosolini
Hyland's effective topos offers an important realizability model for constructive mathematics in the form of a category whose internal logic validates Church's Thesis. It also cont…
The category of equilogical spaces and the effective topos as homotopical quotients
Giuseppe Rosolini
We show that the two models of extensional type theory, those given by the category of equilogical spaces and by the effective topos, are homotopical quotients of categories of 2-g…