The category of equilogical spaces and the effective topos as homotopical quotients

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-groupoids

Quotient completion for the foundation of constructive mathematics

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 type theory. The key concept we employ is that of a Lawvere hyperdoctrine for which we describe a notion of quotient completion. That notion includes the exact completion on a category with weak finite limits as an instance as well as examples from type theory that fall apart from this.Comment: 32 page

Elementary quotient completion

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 effective quotients and extensional equality. We note that the elementary quotient completion can be obtained as the composite of two free constructions: one adds effective quotients, and the other forces extensionality of maps. We also prove that each construction preserves comprehensions

Lo status giuridico dell'insegnante di religione cattolica tra vecchia e nuova normativa

Il presente lavoro affronta la problematica dello status giuridico dell'insegnate di religione cattolica. Una figura atipica all'interno della scuola in quanto caratterizzata dalla duplice competenza dell'autorità ecclesiastica e dell'autorità scolastica. Attraverso il susseguirsi delle disposizioni normative si evince una sempre più chiara parificazione dell'Idr ai docenti di materie curricolari

A comonad for Grothendieck fibrations

We study the 2-category theory of Grothendieck fibrations in the 2-category of functors \ct{Cat}^{\ct{2}}. After redrawing a few general results in that context, we show that fibrations over a given base are pseudo-coalgebras for a 2-comonad on \ct{Cat} / \ct{B}. We use that result to explain how an arbitrary fibration is equivalent to one with a splitting