Adjoint functors
Universal morphisms induce hom-set adjunction

Given a right adjoint functor G : C → D; in the sense of initial morphisms, one may construct the induced hom-set adjunction by doing the following steps.

A similar argument allows one to construct a hom-set adjunction from the terminal morphisms to a left adjoint functor. (The construction that starts with a right adjoint is slightly more common, since the right adjoint in many adjoint pairs is a trivially defined inclusion or forgetful functor.)
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