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Connected limits, familial representability and Artin glueing

Published online by Cambridge University Press:  04 March 2009

Aurelio Carboni  and
Peter Johnstone
Aurelio Carboni
Affiliation:
Dipartimento di Matematica, Università di Genova, Italy.
Peter Johnstone
Affiliation:
Department of Pure Mathematics, University of Cambridge, England.
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Abstract

We consider the following two properties of a functor F from a presheaf topos to the category of sets: (a) F preserves connected limits, and (b) the Artin glueing of F is again a presheaf topos. We show that these two properties are in fact equivalent. In the process, we develop a general technique for associating categorical properties of a category obtained by Artin glueing with preservation properties of the functor along which the glueing takes place. We also give a syntactic characterization of those monads on Set whose functor parts have the above properties, and whose units and multiplications are cartesian natural transformations.

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Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 4 , December 1995 , pp. 441 - 459
Copyright
Copyright © Cambridge University Press 1995

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