* Preprint: Flatness, preorders and general metric spaces
@ 2003-09-18 10:56 V. Schmitt
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From: V. Schmitt @ 2003-09-18 10:56 UTC (permalink / raw)
To: categories
Dear all, I put a recent paper (just submitted)
in the math Arxiv at
http://front.math.ucdavis.edu/math.CT/0309209
Your comments are most welcome.
Thanks.
Vincent.
*Title:* Flatness, preorders and general metric spaces
*Author:* Vincent Schmitt <http://front.math.ucdavis.edu/author/Schmitt-V*>
*Categories:* CT Category Theory <http://front.math.ucdavis.edu/math.CT>
*Abstract:* This paper studies a general notion of 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 Flat_P(A) of P-flat presheaves over A. This
completion is related to the free cocompletion of A under a class of
colimits defined by Kelly. For a category A, for P = P0 the class of
all presheaves, Flat_P0(A) is the Cauchy-completion of A. Two
classes P1 and P2 of interest for general metric spaces are
considered. The P1- and P2-flatness are investigated and the
associated completions are characterized for general metric spaces
(enrichemnts over R+) and preorders (enrichments over Bool). We get
this way two non-symmetric completions for metric spaces and
retrieve the ideal completion for preorders.
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