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Let A be an abelian category and let $A \in $ A. Denote by InjA the category of injective objects of A. We denote by $A\langle0\rangle$ the complex concentrated in degree zero. I define an injective resolution to be a complex $B$ in InjA quasi-isomorphic to $A\langle0\rangle$.

Question. Is this equivalent to the regular definition or do I need to specify that $B^i = 0$ for $i<0$? If this is obvious, I apologise. I am tired right now.

aaron
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    Unless your definition of "complex" excludes negative degrees, this is an extra condition in general. – Zhen Lin Oct 06 '14 at 07:30
  • Are you the same aaron as aaron ? I mean, with "Is the cokernel of the pullback-pushforward of a coherent sheaf in the image of the pushforward on the complement" ? – Dietrich Burde Dec 05 '14 at 19:26

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