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Regular functors and relative realisability categories

Published online by Cambridge University Press:  18 April 2013

WOUTER PIETER STEKELENBURG
WOUTER PIETER STEKELENBURG*
Affiliation:
Utrecht University, Department of Mathematics, P.O. Box 80010, 3508 TA Utrecht, The Netherlands Email: w.p.stekelenburg@gmail.com
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Abstract

The relative realisability toposes introduced by Awodey, Birkedal and Scott in Awodey et al. (2002) satisfy a universal property involving regular functors to other categories. We use this universal property to define what relative realisability categories are when they are based on categories other than the topos of sets. This paper explains the property and gives a construction for relative realisability categories that works for arbitrary base Heyting categories. The universal property also provides some new geometric morphisms to relative realisability toposes.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Issue 5 , October 2013 , pp. 1082 - 1110
Copyright
Copyright © Cambridge University Press 2013 

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