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luw
luw
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Let A$\mathcal{A}$ be an Abelian category, X$X$ be a complex, F$F$ be a contravariant exact functor. I am wondering whether F preserves the homology of X, that means whether H^{i}(FX)=F(H^{-i}(X)) \forall i$H^{i}(FX)=F(H^{-i}(X)),\ \forall i$? (Obviously, this is true for covariant functors)

Let A be an Abelian category, X be a complex, F be a contravariant exact functor. I am wondering whether F preserves the homology of X, that means whether H^{i}(FX)=F(H^{-i}(X)) \forall i? (Obviously, this is true for covariant functors)

Let $\mathcal{A}$ be an Abelian category, $X$ be a complex, $F$ be a contravariant exact functor. I am wondering whether F preserves the homology of X, that means whether $H^{i}(FX)=F(H^{-i}(X)),\ \forall i$? (Obviously, this is true for covariant functors)

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luw
luw
  • 327
  • 1
  • 6

homology under exact functors

Let A be an Abelian category, X be a complex, F be a contravariant exact functor. I am wondering whether F preserves the homology of X, that means whether H^{i}(FX)=F(H^{-i}(X)) \forall i? (Obviously, this is true for covariant functors)