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Pré-Publication, Document De Travail Année : 2022

A lemma for microlocal sheaf theory in the $\infty$-categorical setting

Pierre Schapira

Résumé

Microlocal sheaf theory of \cite{KS90} makes an essential use of an extension lemma for sheaves due to Kashiwara, and this lemma is based on a criterion of the same author giving conditions in order that a functor defined in $\mathbb{R}$ with values in the category $Sets$ of sets be constant. In a first part of this paper, using classical tools, we show how to generalize the extension lemma to the case of the unbounded derived category. In a second part, we extend Kashiwara's result on constant functors by replacing the category $Sets$ with the $\infty$-category of spaces and apply it to generalize the extension lemma to $\infty$-sheaves, the $\infty$-categorical version of sheaves. Finally, we define the micro-support of sheaves with values in a stable $(\infty,1)$-category.

Dates et versions

hal-03840018 , version 1 (04-11-2022)

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Citer

Marco Robalo, Pierre Schapira. A lemma for microlocal sheaf theory in the $\infty$-categorical setting. 2022. ⟨hal-03840018⟩
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