Properties
- The direct image functor is right adjoint to the inverse image functor, which means that for any continuous and sheaves respectively on X, Y, there is a natural isomorphism:
- .
- If f is the inclusion of a closed subspace X ⊂ Y then f∗ is exact. Actually, in this case f∗ is an equivalence between sheaves on X and sheaves on Y supported on X.
Read more about this topic: Direct Image Functor
Famous quotes containing the word properties:
“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)
“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)