Sheaf Extension - Properties

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

Other articles related to "properties":

Kiawah Island, South Carolina - Real Estate Market
... Many of the Kiawah Island properties are located directly on the beach or just a short distance away, and there are numerous golf course properties and lagoon view properties as ...
Geophysics - Physical Phenomena - Mineral Physics
... Further information Mineral physics The physical properties of minerals must be understood to infer the composition of the Earth's interior from seismology ... Mineral physicists study the elastic properties of minerals their high-pressure phase diagrams, melting points and equations of state at high pressure and the ... Water is a very complex substance and its unique properties are essential for life ...
Zamak 4
0.04 - - - - - - - - max 4.2 0.4 0.05 0.003 0.002 0.001 0.02 0.001 0.02 0.0005 0.001 Zamak 4 properties Property Metric value English value Mechanical properties Ultimate tensile strength 317 MPa ...

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)