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Exact completion and constructive theories of sets
Stockholm University, Faculty of Science, Department of Mathematics. (Logic)
Stockholm University, Faculty of Science, Department of Mathematics. (Logic)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In the present paper we use the theory of exact completions to study categorical properties of small setoids in Martin-Loef type theory and, more generally, of models of the Constructive Elementary Theory of the Category of Sets, in terms of properties of their subcategories of choice objects (i.e. objects satisfying the axiom of choice). Because of these intended applications, we deal with categories that lack equalisers and just have weak ones, but whose objects can be regarded as collections of global elements. In this context, we study the internal logic of the categories involved, and employ this analysis to give a sufficient condition for the local cartesian closure of an exact completion. Finally, we apply this result to show when an exact completion produces a model of CETCS.

Keywords [en]
setoids, exact completion, local cartesian closure, constructive set theory, categorical logic
National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-151876OAI: oai:DiVA.org:su-151876DiVA, id: diva2:1176023
Available from: 2018-01-19 Created: 2018-01-19 Last updated: 2018-01-21Bibliographically approved

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