Flatness, accessibility and metric spaces

Details Flatness, accessibility and metric spaces Flatness, accessibility and metric spaces

2004-03-09

arxiv.org/abs/math/0403164v1

Mathematics

Category Theory

A new version of the paper math.CT/0309209 that contains results regarding accessible categories in the enriched context

Scientific paper

This paper studies a notion of parameterized flatness in the enriched context: p-flatness where the parameter p stands for a class of presheaves. One obtains a completion of a category A by considering the category F_p(A) of p-flat presheaves over A. The completion is related to the free cocompletion under a class of colimits defined by Kelly. We define a notion of Q-accessible categories where Q is the class of p-flat indexes. For a category A, for p = P0 the class of all presheaves, F_P0(A) is the Cauchy-completion of A. Two classes P1 and P2 of interest for general metric spaces and prorders are considered. The F_P1- and F_P2- flatess are characterized yielding non-symmetric completions of metric spaces a la Cauchy involving non-symmetric filters.

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