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Constructing a small category of setoids

Published online by Cambridge University Press:  13 September 2011

OLOV WILANDER
OLOV WILANDER*
Affiliation:
Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden Email: wilander@math.uu.se
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Abstract

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Consider the first-order theory of a category.d It has a sort of objects, and a sort of arrows (so we may think of it as a small category). We show that, assuming the principle of unique substitutions, the setoids inside a type theoretic universe provide a model for this first-order theory. We also show that the principle of unique substitutions is not derivable in type theory, but that it is strictly weaker than the principle of unique identity proofs.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 22 , Issue 1 , February 2012 , pp. 103 - 121
Copyright
Copyright © Cambridge University Press 2011

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