Definition
Let X be a scheme, and let F, H be sheaves (of modules) on X. An extension of H by F is a short exact sequence of sheaves
Note that an extension is not determined by the sheaf G alone: The morphisms are also important.
A simple example of an extension of H by F is the sequence
where the second arrow is the inclusion and the fourth arrow is the projection onto the second summand. This extension is sometimes called trivial.
Read more about this topic: Sheaf Extension
Famous quotes containing the word definition:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)