Theorem 5.5 (0MV2) · ScalingStacks

Theorem 5.5. Under the hypotheses of Setup 5.1, the functor

\textnormal{Hom}(S,-):\mathcal{C}\rightarrow\textnormal{Mod}(k^{\textnormal{op% }}),

is an equivalence of categories, and hence, the coheart $\mathcal{C}$ of the non-degenerate co- $t$ -structure obtained in Theorem 4.1 is an abelian category.

0MV3

Proof: By Lemma 5.2 and Proposition 5.4, $\textnormal{Hom}(S,-)$ is dense and fully faithful. Hence, by [14, Theorem IV.4.1], $\textnormal{Hom}(S,-)$ is an equivalence of categories. $\Box$

David Pauksztello

Original source: arXiv:0705.0102v2