2004/03/09 by Vincent Schmitt, Schmitt, Vincent
Mathematics · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.CT
paper · pdf · doi:10.48550/arxiv.math/0403164
A new version of the paper math.CT/0309209 that contains results regarding accessible categories in the enriched context
arxiv created 2004/03/09 · openalex publication_date 2004/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Fp(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, FP0(A) is the Cauchy-completion of A. Two classes P1 and P2 of interest for general metric spaces and prorders are considered. The FP1- and FP2- flatess are characterized yielding non-symmetric completions of metric spaces a la Cauchy involving non-symmetric filters.