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Three extensional models of type theory

Published online by Cambridge University Press:  01 April 2009

BENNO VAN DEN BERG
BENNO VAN DEN BERG*
Affiliation:
Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstrasse 7, 64289 Darmstadt, Germany Email: berg@mathematik.tu-darmstadt.de
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Abstract

We compare three categorical models of type theory with extensional constructs: setoids over extensional type theory; setoids over intensional type theory and a certain free exact category (the free ‘ΠW-pretopos’). By studying the amount of choice available in these categories, we are able show that they are distinct.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 19 , Issue 2 , April 2009 , pp. 417 - 434
Copyright
Copyright © Cambridge University Press 2009

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