Geodesic
Presentations of clusters and strict free-cocompletions
Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 492-513

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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.

Publié le :
Classification : 18A35
Keywords: precluster, cluster, cocompletion 
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Erwan Beurier; Dominique Pastor; René  Guitart. Presentations of clusters and strict free-cocompletions. Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 492-513. http://geodesic.mathdoc.fr/item/TAC_2021_36_a16/