1. Similarly, the maps f and p induce maps of differential graded coalgebras 2. Moreover a natural transformation between two such functors induces a homotopy between the induced maps . 3. Soon after Floer's introduction of Floer homology, Donaldson realized that cobordisms induce maps . 4. The differential or pushforward of a map between manifolds is the induced map between tangent spaces of those maps. 5. The argument passes " E " to the induced map \ Phi _ E and uses completely positive. 6. For example, over the integers, the pairing is nondegenerate but not unimodular, as the induced map from to is multiplication by 2. 7. In this case, the phrase " induced map " would have a subjective meaning, depending on context to establish what particular process we mean. 8. A morphism is monic if and only if the induced map , defined by for all morphisms, is injective for all " Z ". 9. There exists a map f : Z \ rightarrow X such that the induced map f _ \ ast on the fundamental groups is same as \ phi 10. In algebraic topology, a "'phantom map "'is a map between spectra such that the induced map between homology theories is zero.
