63 research outputs found
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
Preface Volume 29
AbstractThis volume contains the proceedings of the 8th conference on Category Theory and Computer Science (CTCS '99) which was held in Edinburgh, UK, from September 10 to September 12, 1999.The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory. While the emphasis is upon applications of category theory, it is recognized that the area is highly interdisciplinary.Previous meetings have been held in Guildford (Surrey), Edinburgh, Manchester, Paris, Amsterdam, Cambridge, and S. Margherita Ligure (Genova).Out of 39 submissions the Programme Committe has selected 19 for presentation at the Conference. The programme also included invited talks by Ryu Hasegawa (Tokyo), Peter Freyd (Pennsylvania), Marcelo Fiore (Sussex), Doug Smith (Kestrel Institute).We wish to thank the anonymous referees and the Programme Committee members: Jiri Adamek, Nick Benton, Rick Blute, Thierry Coquand, Martin Escardo, Masahito Hasegawa, Martin Hofmann (Chair), Peter O'Hearn, Dusko Pavlovic, Horst Reichel, Giuseppe Rosolini, Andre Scedrov.We also wish to thank the ENTCS editor Michael Mislove for encouragement and technical support
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'autoritĂ ecclesiastica e dell'autoritĂ scolastica. Attraverso il susseguirsi delle disposizioni normative si evince una sempre piĂč 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
Dagli insiemi alle categorie
Si presenta una descrizione della teoria delle categorie con alcuni sviluppi in ambito logico-matematico
- âŠ