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Cocompleteness over coverings

Part of: General theory of categories and functors Categories with structure Categories and geometry

Published online by Cambridge University Press:  09 April 2009

Renato Betti
Renato Betti
Affiliation:
Dipartimento di Matematica Università di Milano via C. Saldini, 50 20133 Milano, Italy
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Abstract

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For enriched categories the correct notion of limit involves indexing by a module. This paper studies the question of cocompletion for a given set of indexing modules. As well as providing a simplified treatment of cocompleteness for ordinary categories, associated sheaves and associated stacks are also included as cocompletion processes for appropriate bases. In fact the saturation of a general set of indexing modules has properties which justify our use of the term “covering” for members of the saturation.

MSC classification

Secondary: 18D20: Enriched categories (over closed or monoidal categories) 18A35: Categories admitting limits (complete categories), functors preserving limits, completions 18F20: Presheaves and sheaves
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 2 , October 1985 , pp. 169 - 177
Copyright
Copyright © Australian Mathematical Society 1985

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