Cocompleteness over coverings
- 1 October 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 39 (2) , 169-177
- https://doi.org/10.1017/s1446788700022448
Abstract
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.Keywords
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