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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.

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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