| 1. | In fact no function of any kind from to is injective.
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| 2. | However, computing sheaf cohomology using injective resolutions is nearly impossible.
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| 3. | Is rationally injective then the Novikov-conjecture holds for G.
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| 4. | Hence the homomorphism is, in general, not injective.
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| 5. | There are multiple other methods of proving that a function is injective.
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| 6. | Multivalued functions often arise as inverses of functions that are not injective.
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| 7. | In general, the representation is neither injective nor surjective.
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| 8. | It can also be dualized, leading to injective modules.
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| 9. | When the degrees are finite, injective is equivalent here to bijective.
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| 10. | In particular ? is injective so homology of dimension 2 also vanishes.
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