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nPOV: Cohomology and derived functors

In the nPOV, cohomology is realized as the connected component of the derived hom space [1]. Namely, $$H^n(X,Y) = \pi_0 \mathbb{H}(X,B^nY),$$ where $\mathbb{H}$ is an $(\infty,1)$-topos and $B$ is the …
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Unifying "cohomology groups classify extensions" theorems

This is not an answer, but just some pointers to things I guess are related! I posted this in the comments, but it got really messy. So I moved it here. -- original comments below -- I also want to …
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