  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 $\Lambda$-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.
