We recall the notions of a graded cocategory, conilpotent cocategory, morphisms of such (cofunctors), coderivations and define their analogs in 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 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.
Keywords: Cocategory, cofunctor, coderivation, filtration
2020 MSC: 18G70; 18D15
Theory and Applications of Categories, Vol. 35, 2020, No. 47, pp 1726-1770.