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Simply Connected Limits

Published online by Cambridge University Press:  20 November 2018

Robert Paré
Robert Paré*
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, N.S., B3H 3J5
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The importance of finite limits in completeness conditions has been long recognized. One has only to consider elementary toposes, pretoposes, exact categories, etc., to realize their ubiquity. However, often pullbacks suffice and in a sense are more natural. For example it is pullbacks that are the essential ingredient in composition of spans, partial morphisms and relations. In fact the original definition of elementary topos was based on the notion of partial morphism classifier which involved only pullbacks (see [6]). Many constructions in topos theory, involving left exact functors, such as coalgebras on a cotriple and the gluing construction, also work for pullback preserving functors. And pullback preserving functors occur naturally in the subject, e.g. constant functors and the Σα. These observations led Rosebrugh and Wood to introduce partial geometric morphisms; functors with a pullback preserving left adjoint [9]. Other reasons led Kennison independently to introduce the same concept under the name semi-geometric functors [5].

Keywords

18A3018B4055Q05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 4 , 01 August 1990 , pp. 731 - 746
Copyright
Copyright © Canadian Mathematical Society 1990

References

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