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Different definitions of derived functors
In principle one uses the notion of derived category, and the other doesn't.
Suppose $F: \mathcal A \to \mathcal B$ is a left exact (additive) functor between abelian categories, and suppose the ...
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Why is the derived tensor product only defined for bounded above derived categories?
In "Residues and Duality" by Hartshorne, the derived tensor $\otimes$ only defined for the bounded above categories (see Chapter II, section 4, p.93), that is one has
$$\otimes: D^{-}(X) \...
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