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Three extensional models of type theory

  • BENNO VAN DEN BERG (a1)

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.

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Three extensional models of type theory

  • BENNO VAN DEN BERG (a1)

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