Morita theory for stable derivators
S Virili - arXiv preprint arXiv:1807.01505, 2018 - arxiv.org
arXiv preprint arXiv:1807.01505, 2018•arxiv.org
We give a general construction of realization functors for $ t $-structures on the base of a
strong stable derivator. In particular, given such a derivator $\mathbb D $, a $ t $-structure
$\mathbf t=(\mathcal D^{\leq0},\mathcal D^{\geq0}) $ on the triangulated category $\mathbb
D (\mathbb 1) $, and letting $\mathcal A=\mathcal D^{\leq0}\cap\mathcal D^{\geq0} $ be its
heart, we construct, under mild assumptions, a morphism of prederivators\[\mathrm {real} _
{\mathbf t}\colon\mathbf {D} _ {\mathcal A}\to\mathbb D\] where $\mathbf {D} _ {\mathcal A} …
strong stable derivator. In particular, given such a derivator $\mathbb D $, a $ t $-structure
$\mathbf t=(\mathcal D^{\leq0},\mathcal D^{\geq0}) $ on the triangulated category $\mathbb
D (\mathbb 1) $, and letting $\mathcal A=\mathcal D^{\leq0}\cap\mathcal D^{\geq0} $ be its
heart, we construct, under mild assumptions, a morphism of prederivators\[\mathrm {real} _
{\mathbf t}\colon\mathbf {D} _ {\mathcal A}\to\mathbb D\] where $\mathbf {D} _ {\mathcal A} …
We give a general construction of realization functors for -structures on the base of a strong stable derivator. In particular, given such a derivator , a -structure on the triangulated category , and letting be its heart, we construct, under mild assumptions, a morphism of prederivators
where is the natural prederivator enhancing the derived category of . Furthermore, we give criteria for this morphism to be fully faithful and essentially surjective. If the -structure is induced by a suitably "bounded" co/tilting object, is an equivalence. Our construction unifies and extends most of the derived co/tilting equivalences appeared in the literature in the last years.
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