Properties
As with group extensions, if we fix F and H, then all (equivalence classes of) possible extensions of H by F form an abelian group. This group is isomorphic to the Ext group, where the identity element in corresponds to the trivial extension.
In the case where H is the structure sheaf, we have, so the group of extensions of by F is also isomorphic to the first sheaf cohomology group with coefficients in F.
Read more about this topic: Sheaf Extension
Famous quotes containing the word properties:
“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)