REALIZATION THEOREMS FOR CATEGORIES OF GRADED MODULES OVER SEMIGROUP-GRADED RINGS

We present a collection of finitely generated projective generators fo r the category of graded modules over a unital semigroup-graded ring. Consequences of the existence of such a collection, as well as other m odule-theoretic results, will arise from more general constructions in volving TTF classes inside Grothendieck categories. For instance, we o btain a description of the category of graded modules whose support li es within a given subset of the semigroup.