Derived functor

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Pythagoras0 (토론 | 기여)님의 2020년 12월 27일 (일) 18:50 판 (→‎메타데이터: 새 문단)
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introduction

  • basic tool to define cohomology theory
  • extend a left invariant functor to get a derived functor
  • then we get a cohomology theory
  • e.g. sheaf cohomology of a topological space X with coefficients in a sheaf \(\mathcal F\) = the right derived functor of the global section functor


left invariant functors

global section functor

  • a functor from sheaves on \(X\) to abelian groups defined by

\[ \mathcal F \mapsto H^{0}(X, \mathcal F) \]

invariants

  • \(G\) : group
  • from modules of \(G\) to abelian groups

\[ M\mapsto M^{G} \]


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