| 1. | Likewise, monoid homomorphisms are just functors between single object categories.
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| 2. | This gives a homomorphism from de Rham cohomology to singular cohomology.
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| 3. | Here, ? is the natural homomorphism into the double dual.
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| 4. | This defines an equivalence relation on the set of almost homomorphisms.
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| 5. | The composition of an antihomomorphism with a homomorphism gives another antihomomorphism.
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| 6. | These are just the rng homomorphisms that map everything to 0.
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| 7. | However, the standard homomorphism may be zero in some cases.
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| 8. | Algebraic structures, with their associated homomorphisms, form mathematical categories.
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| 9. | In the case of groups, the morphisms are the group homomorphisms.
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| 10. | Functors between one-object categories correspond to monoid homomorphisms.
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