On cohomotopy-type functors

This article deals with Chogoshvili cohomotopy functors which are defined by extending a cohomology functor given on some special auxiliary subcategories of the category of topological spaces. The question of choosing these subcategories is discussed. In particular, it is shown that in the singular case to define absolute groups it is sufficient that auxiliary subcategories should have as objects only spheresSn, Moore spacesPn(t)=Sn−1 Ut en, and one-point unions of these spaces.