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Setoids and universes

Published online by Cambridge University Press:  07 April 2010

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

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Setoids commonly take the place of sets when formalising mathematics inside type theory. In this note, the category of setoids is studied in type theory with universes that are as small as possible (and thus, the type theory is as weak as possible). In particular, we will consider epimorphisms and disjoint sums. We show that, given the minimal type universe, all epimorphisms are surjections, and disjoint sums exist. Further, without universes, there are countermodels for these statements, and if we use the Logical Framework formulation of type theory, these statements are provably non-derivable.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Issue 4 , August 2010 , pp. 563 - 576
Copyright
Copyright © Cambridge University Press 2010

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