Notes on enriched categories with colimits of some class

G. M. Kelly; V. Schmitt

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arXiv · math/0501383

Notes on enriched categories with colimits of some class

G. M. Kelly·V. Schmitt

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Abstract

Given a class Phi of weights, we study the following classes: Phi^+ of Phi-flat weights which are the psi for which psi-colimits commute in the base V with limits with weights in Phi; and Phi^-, dually defined, of weights psi for which psi-limits commute in the base V with colimits with weights in Phi. We show that both these classes are saturated (i.e. closed under the terminology of Albert-Kelly or Betti's coverings). We prove that for the class P of all weights P^+ = P^-. For any small B, we defined an enriched adjunction a` la Isbell [B,V]^op -> [B^op,V] and show how it restricts to an equivalence (P^-(B^op))^op ~ P^-(B) between subcategories of small projectives.

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BibTeX RIS

G. M. Kelly, V. Schmitt. 2005-01-22. Notes on enriched categories with colimits of some class. https://arxiv.org/abs/math/0501383

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