Enriched accessible categories

Borceux, Francis;Quinteriro, C
(1996) Bulletin of the Australian Mathematical Society — Vol. 54, n° 3, p. 489-501 (1996)

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Authors
  • Borceux, FrancisUCLouvain
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  • Quinteriro, C
    Author
Abstract
We consider category theory enriched in a locally finitely presentable symmetric monoidal closed category V. We define the V-filtered colimits as those colimits weighted by a V-flat presheaf and consider the corresponding notion of V-accessibIe category. We prove that V-accessible categories coincide with the categories of V-flat presheaves and also with the categories of V-points of the categories of V-presheaves. Moreover, the V-locally finitely presentable categories are exactly the V-cocomplete finitely accessible ones. To prove this last result, we show that the Cauchy completion of a small V-category C is equivalent to the category of V-finitely presentable V-flat presheaves on C.
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Borceux, F., & Quinteriro, C. (1996). Enriched accessible categories. Bulletin of the Australian Mathematical Society, 54(3), 489-501. https://doi.org/10.1017/S0004972700021900 (Original work published 1996)