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Jul 4, 2018 at 12:33 comment added Mark Grant You're right, they are transfer maps. A reference I should have included in my answer is sections VII.7 and VII.8 of Brown's "Cohomology of Groups".
Jul 4, 2018 at 11:28 vote accept Dominic Else
Jul 4, 2018 at 11:24 comment added Dominic Else Thanks for this really helpful answer! In the regular $G$-complex case, do you have any hints for how I can think of the sheaf restriction morphism $F^q(G_{\sigma'}) \to F^q(G_{\sigma})$ associated with the inclusion $\sigma \to \sigma'$? I don't think it just comes from the inclusion $G_{\sigma'} \leq G_{\sigma}$ -- that would go in the other direction.
Jun 28, 2018 at 7:19 history edited Mark Grant CC BY-SA 4.0
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Jun 27, 2018 at 14:26 history answered Mark Grant CC BY-SA 4.0