graded comonoid
Graded comonoids as oplax functors. Equivalently, a graded comonoid is an oplax monoidal functor from the monoid seen as a monoidal category. See Grading monads, comonads, distributive laws (Uustalu).
Graded comonoids via graded spaces. Graded comonoids are comonoids in a duoidal category of graded objects for a monoidal category with products preserved by the tensor; one needs to be careful at using the opposite category instead of opposite graded monoids. A less complicated point of view is that of graded comonoids as oplax functors.
Tags: comonoid, graded comonad, graded monoid, duoidal category.