Filtered cocategories

2020/10/11 by Volodymyr Lyubashenko, Lyubashenko, Volodymyr
Mathematics · #18D15 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:18D15

paper · pdf · doi:10.48550/arxiv.2010.05242

45 pp, LaTeX 2e, AmsLatex, dsfont.sty, euscript.sty, hyperref.sty, Paul Taylor's diagrams.sty

arxiv created 2020/10/11 · arxiv updated 2020/10/13

Abstract

We recall the notions of a graded cocategory, conilpotent cocategory, morphisms of such (cofunctors), coderivations and define their analogs in \mathbb L-filtered setting. The difference with the existing approaches: we do not impose any restriction on Λ-modules of morphisms (unlike Fukaya and collaborators), we consider a wider class of filtrations than De~Deken and Lowen (including directed groups \mathbb L). Results for completed filtered conilpotent cocategories include: cofunctors and coderivations with value in completed tensor cocategory are described, a partial internal hom is constructed as the tensor cocategory of certain coderivation quiver, when the second argument is a completed tensor cocategory.

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