Dear Colin, Can I ask a technical question about foundations here? Does the "enough injectives" result assume a classical base theory? The classical result for module categories uses choice, and my understanding is that the result for sheaf categories uses Barr covers to make available the classical result. I wonder if there's an unequivocally constructive formulation. Regards, Steve. Colin McLarty wrote:
AG intended this paper to hit the very center of homological algebra: from now on homological algebra is about derived functors on Abelian categories with enough injectives -- and he justifies this by proving (against the general expectation) that all sheaf categories have enough injectives . Of course there are other resolutions besides injective, we will use them too, but they are special cases for special purposes.
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