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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: [email protected]
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Abstract

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.

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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