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
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