| 21. | The idea of an adjoint functor was formulated by Daniel Kan in 1958.
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| 22. | This functor is left adjoint to the forgetful functor from groups to sets.
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| 23. | This functor is left adjoint to the forgetful functor from groups to sets.
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| 24. | This functor has a left adjoint which is the integral group ring construction.
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| 25. | Such a functor is necessarily injective on objects up-to-isomorphism.
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| 26. | A full and faithful functor is necessarily injective on objects up to isomorphism.
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| 27. | This construction makes simplicial homology a functor from simplicial complexes to abelian groups.
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| 28. | The two variants are related by an adjoint functor.
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| 29. | The direct image functor is left exact, but usually not right exact.
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| 30. | A functor into \ widehat { C } is sometimes called a profunctor.
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