Enriched accessible categories
We consider category theory enriched in a locally finitely presentable symmetric monoidal closed category ν. We define the ν-filtered colimits as those colimits weighted by a ν-flat presheaf and consider the corresponding notion of ν-accessible category. We prove that ν-accessible categories coincid...
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Veröffentlicht in: | Bulletin of the Australian Mathematical Society 1996-12, Vol.54 (3), p.489-501 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | We consider category theory enriched in a locally finitely presentable symmetric monoidal closed category ν. We define the ν-filtered colimits as those colimits weighted by a ν-flat presheaf and consider the corresponding notion of ν-accessible category. We prove that ν-accessible categories coincide with the categories of ν-flat presheaves and also with the categories of ν-points of the categories of ν-presheaves. Moreover, the ν-locally finitely presentable categories are exactly the ν-cocomplete finitely accessible ones. To prove this last result, we show that the Cauchy completion of a small ν-category Cis equivalent to the category of ν-finitely presentable ν-flat presheaves on C. |
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ISSN: | 0004-9727 1755-1633 |
DOI: | 10.1017/S0004972700021900 |