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Enriched accessible categories

Published online by Cambridge University Press:  17 April 2009

Francis Borceux  and
Carmen Quinteriro
Francis Borceux
Affiliation:
Departement de Mathematiques, Universite de Louvain, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium
Carmen Quinteriro
Affiliation:
Universidade de Vigo, Facultade de Ciencias Económicas e Empresariais, Lagoas – Marcosende s/n, 36200 Vigo, Spain
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 489 - 501
Copyright
Copyright © Australian Mathematical Society 1996

References

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