In thio paper, we consider both homotopy and sheaf theory and construct an algebraic sheaf by means of the H-cogroups. Finally, we give some algebraic topological characterizations. 1. The Sheaf of the Groups formed by H-Cogroups över topological spaces. ‘ Lct’s recall the following definition, Definition 1.1. Let S be two topological spaces, and tz: S X be a locally topological map. Then the pair (S, k) or shortly S is c aile d a sheaf över X. Let (5 be the category of topological spaces X satisfying the pro- perty that ali pointed topological spaces (X,x) with x e İL have the same homotopy type. This category inciudes for example ali topological vector spaces. Let us take xe(5 as a base set if Q is any H-cogroup, then the set of homotopy class of homotop maps preserving the base points from (Q,qo) to (X,Xi), iel, [Q; (X,Xi)] obtained for each xeX, (X,x) pointed topological spaces. i.e, P(X) = V [Q; (X,x)]. Thus P(X) is a set över