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As i read the literature, derived functors were there several years before derive categories - right?

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I believe so. My understanding was derived functors go back to Cartan-Eilenberg (1950s) and derived categories to Verdier (1960s). But I can't claim to be an expert. – Donu Arapura Mar 3 '12 at 14:10
Donu is correct. Derived functors were the motivation for derived categories. – Steven Landsburg Mar 3 '12 at 15:36
I think is this provides some background between the homological/homotopical algebra and the derived cat communities. Some of us didn't pick up on the derived cat language, but charged ahead using resolutions and the yoga that one resolution was as good as another - e.g the bar resolution and relatives. – Jim Stasheff Mar 3 '12 at 16:18

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