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