Monoidal infinity category of complexes from Tannakian viewpoint |
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Authors: | Hiroshi Fukuyama Isamu Iwanari |
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Affiliation: | 1. Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan 2. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan
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Abstract: | In this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable $infty $ -categories of quasi-coherent complexes. It can be viewed as a derived analogue of Tannaka duality. As a consequence, we deduce that an algebraic stack satisfying a certain condition can be recovered from the symmetric monoidal stable $infty $ -category of quasi-coherent complexes with tensor operation. |
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