bio | website | preschema.com |
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location | Essen, Germany | |

age | 23 | |

visits | member for | 5 years, 6 months |

seen | Jun 18 at 14:21 | |

stats | profile views | 1,541 |

Jun 18 |
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Higher refinement of Seifert-van Kampen theorem on the language of hocolim
@DavidRoberts, Lurie's version is discussed here: ncatlab.org/nlab/show/higher+homotopy+van+Kampen+theorem |

May 25 |
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is there a moduli of stable infinity categories?
@pro, thanks. I know that moduli stacks of dg-categories are discussed in To\"en's beautiful paper on derived Azumaya algebras, which has been generalized to a spectral stack parametrizing R-linear categories for R a commutative ring spectrum by Antieau-Gepner. I don't think they discuss the type of issue you are interested in there, though. |

May 24 |
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Homotopy pullback preserving functor
@FernandoMuro, I may be missing something, but if $A$ and $B$ have the trivial model structures, then the condition of preserving fibrations and weak equivalences is vacuous, while the condition of preserving homotopy fibres is a type of left-exactness, right? |

May 24 |
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Homotopy pullback preserving functor
@FernandoMuro, the proposition in the paper says that the functor preserves fibrations in the model structure, not fibre sequences. |

May 24 |
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is there a moduli of stable infinity categories?
@pro, thanks! Would you mind also sharing the approximations that you found in the literature? |

May 24 |
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is there a moduli of stable infinity categories?
@pro, would you mind explaining what you mean by infinitesimal theory here? |

Apr 28 |
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Is there any explicit result on the triangulated category of singularities of a curve?
Do you know a reference for that? I only knew that fact in the smooth case. |

Apr 28 |
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Is there any explicit result on the triangulated category of singularities of a curve?
Just a comment: a semi-orthogonal decomposition of D^b_coh induces a semi-orthogonal decomposition of D_sg, according to Corollary 1.12 here. |

Apr 22 |
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Are Bökstedt's THH manuscripts available?
I could e-mail them to you. |

Apr 9 |
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Algebraic K-theory of complex varieties
Analytic descent for K-theory would follow directly from analytic descent for perfect complexes. I have no idea whether the latter is true, though. |

Apr 6 |
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Integral transform on noncommutative spaces
@bananastack, I learned this from Marco Robalo's thesis, but it is probably in some paper of To\"en. |

Apr 6 |
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How does one compute a colimit of monoidal categories?
I believe non-strict monoidal categories can be described as algebras over a monad which is a cofibrant replacement of the monad presenting strict monoidal categories. So a similar statement should hold. |

Apr 6 |
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Integral transform on noncommutative spaces
@bananastack, saturated dg-categories also come from dg-algebras, by the way (from dg-algebras of finite type, even). |

Apr 5 |
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What is the applications of the dg-enhancements of derived categories of sheaves
@ZhenLin, I notice now that this is made precise, in terms of dg-localization, in section 2.4 of To\"en's notes here. |

Apr 4 |
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What is the applications of the dg-enhancements of derived categories of sheaves
@ZhenLin, this wasn't meant to be a precise statement, but one can probably use the dg-localization or also a spectral analogue instead to make it precise. |

Apr 1 |
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NCG with all noncommutativity in a nilpotent ideal
In line with Qiaochu's comment, some aspects of E_n-geometry are studied in the thesis of John Francis and this sequel. |

Mar 30 |
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When is the category of small (pre)sheaves a(n elementary) topos?
According to this paper of Mike Shulman, when $\mathcal{P}C$ is finitely complete, it is an infinitary pretopos, so by Giraud's theorem it is a topos iff it admits a small generating set. |

Mar 27 |
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Is the derived category of perfect complexes idempotent complete?
In the language of infinity-categories, the relevant result is Proposition 5.5.7.8 in Higher Topos Theory. See also Section 2.4 of arxiv.org/pdf/1001.2282.pdf, especially the text right before Lemma 2.20, for a discussion adapted to the stable setting. |

Mar 27 |
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Is the derived category of perfect complexes idempotent complete?
One good reference is Proposition 2.1.1 here: arxiv.org/abs/math/0204218. |

Mar 25 |
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Do algebraic stacks satisfy fpqc descent?
@Niels, for me an algebraic stack is defined to be a sheaf of groupoids (satisfying some conditions), so I interpret the question as whether or not this sheaf satisfies fpqc descent. |