Manifolds, Sheaves, and Cohomology by Torsten Wedhorn

Author:Torsten Wedhorn
Language: eng
Format: epub, pdf
Publisher: Springer Fachmedien Wiesbaden, Wiesbaden

(8.22)

If I is finite, then .

Another special case is the cokernel of a homomorphism of -modules as the colimit of the diagram (). It is denoted by and it is the sheaf associated with the presheaf . By (8.21) we have . In particular, w is a surjective homomorphism of sheaves if and only if .

Let be an -submodule of and let be the inclusion. Then

is called the quotient of by . It is the -module associated with the -premodule .

For a homomorphism of -modules we can also define its image

and its coimage

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