Summary: Type Theory via Exact Categories
Extended abstract
L. Birkedal \Lambda A. Carboni G. Rosolini D.S. Scott
School of Computer Science II Facolt‘a di Scienze MFN DISI School of Computer Science
CMU Univ. di Milano Univ. di Genova CMU
Pittsburgh, USA Como, Italy Genova, Italy Pittsburgh, USA
Abstract
Partial equivalence relations (and categories of
these) are a standard tool in semantics of type theo­
ries and programming languages, since they often pro­
vide a cartesian closed category with extended defin­
ability. Using the theory of exact categories, we give
a category­theoretic explanation of why the construc­
tion of a category of partial equivalence relations of­
ten produces a cartesian closed category. We show
how several familiar examples of categories of partial
equivalence relations fit into the general framework.
1 Introduction
Partial equivalence relations (and categories of
these) are a standard tool in semantics of programming

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University
Birkedal, Lars - Theory Department, IT-Universitetet i København

Collections: Computer Technologies and Information Sciences; Mathematics