Notes on enriched categories with colimits of some class

Details Notes on enriched categories with colimits of some class Notes on enriched categories with colimits of some class

2005-01-22

arxiv.org/abs/math/0501383v1

Mathematics

Category Theory

22 pages. This work is on going. We intend to add further sections to this work in the near future. Results presented here are

Scientific paper

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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