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