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$\begingroup$ Thanks for the answer! For the moment, I understand that people are generally interested in the global sections functor $\Gamma(B)$ and a global section corresponds to a morphism in $\mathrm{Hom}_{\mathrm{Mod}(O)}(O,B)$ (characterised by the image of the unit) or $\mathrm{Hom}_{\mathrm{PSh}(S)}(1,B)$. Is that OK? $\endgroup$

jpvigneaux
– jpvigneaux

2016-12-27 10:11:16 +00:00
Commented Dec 27, 2016 at 10:11
$\begingroup$ Concerning the isomorphism: Proposition 4.6.10 uses Proposition 4.4.10, that is proved by the "Weil procedure" (chasing elements). Weibel does something similar (Acyclic assembly Lemma 2.7.3) and just states the balancing of $\mathrm{Ext}$ for modules. Do you know a book where this is stated in general? $\endgroup$

jpvigneaux
– jpvigneaux

2016-12-27 10:12:00 +00:00
Commented Dec 27, 2016 at 10:12
$\begingroup$ Regarding your first comment, that sounds good to me. Regarding your second comment, I'm not quite sure what general result you're looking for. But I think that a version of Proposition 4.4.10 holding in an arbitrary abelian category should follow just from the Freyd-Mitchell embedding theorem. $\endgroup$

Tim Campion
– Tim Campion

2016-12-28 17:47:03 +00:00
Commented Dec 28, 2016 at 17:47

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