Other Properties
If A is an abelian category and A is an object of A, then HomA(A,–) is a covariant left-exact functor from A to the category Ab of abelian groups. It is exact if and only if A is projective.
Let R be a ring and M a left R-module. The functor HomZ(M,–): Ab → Mod-R is right adjoint to the tensor product functor – R M: Mod-R → Ab.
Read more about this topic: Hom Functor
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“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)