Presentations of clusters and strict free-cocompletions

The clusters considered in this paper are seen as morphisms between small arbitrary diagrams in a given locally small category C. They have initially been introduced to extend to all small diagrams the results for filtered diagrams, by exhibiting a very basic presentation of the formula used in the...

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Bibliographic Details
Published inTheory and applications of categories Vol. 36; no. 17; pp. 492 - 513
Main Authors Beurier, Erwan, Pastor, Dominique, Guitart, René
Format Journal Article
LanguageEnglish
Published Mount Allison University 19.08.2021
SeriesThe Rosebrugh Festschrift - A special volume celebrating Bob Rosebrugh's 25 years as managing editor of TAC
Subjects
Category Theory
Mathematics
cluster
cocompletion
precluster
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Summary:The clusters considered in this paper are seen as morphisms between small arbitrary diagrams in a given locally small category C. They have initially been introduced to extend to all small diagrams the results for filtered diagrams, by exhibiting a very basic presentation of the formula used in the definition of the category Ind(C) of ind-objects in C. They constitute a category Clu (C) which contains Ind(C). We study these clusters, their construction and composition. Thus we provide any user with the means to generate clusters and perform calculations with them. So we can give a simple proof of the fact that Clu (C) is a strict free cocompletion of C for all small diagrams, determined up to isomorphism. We compare it to some other cocompletion problems.
ISSN:1201-561X
1201-561X