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resolution of a sheaf∗
Simone†
2013-03-21 18:06:12
Given a sheaf F on a topological space X and a pair (F • , d• ) where F • =
{F }q∈N is a family of sheaves on X and d• = {dq }q∈N is a family of sheaf
morphisms
dq : F q → F q+1 ,
q
we say that (F • , d• ) is a resolution of F if there exists an injection j : F → F 0
such that the sequence
j
d0
d
0 → F → F 0 → F 1 →1 · · · → F q → . . .
is exact.
∗ hResolutionOfASheafi created: h2013-03-21i by: hSimonei version: h36334i Privacy
setting: h1i hDefinitioni h18G60i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
You can reuse this document or portions thereof only if you do so under terms that are
compatible with the CC-BY-SA license.
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