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Absolute colimits in enriched categories. (English) Zbl 0532.18001

This paper is concerned with conditions, in the enriched case, on an indexing type \(\Phi\) such that every colimit indexed by \(\Phi\) is preserved by all functors (i.e. is absolute). The result proved is the following: If \(\Phi\) is a module (used here to mean the same as others have called bimodule, profunctor, distributor), then every colimit indexed by \(\Phi\) is absolute if and only if \(\Phi\) has a right adjoint in the bicategory of modules.
Reviewer: H.Wolff

MSC:

18A35 Categories admitting limits (complete categories), functors preserving limits, completions
18D20 Enriched categories (over closed or monoidal categories)
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
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References:

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