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Using obstruction theory tools to a pair of spaces two invariants are defined whose vanishing is a necessary and sufficient condition for homotopy classification of certain maps between these spaces by the induced cohomology and homotopy homomorphisms respectively. 2. Definitions. All spaces in this paper are pathwise connected, basepointed, and have the homotopy type of CW-complexes. All maps and homotopies will preserve basepoints. Y will be simply connected, and we use the following notationdoi:10.2307/2037939 fatcat:hv5ltkwbvndttllae4gsq74qbq