Localizations and completions of stable $\infty$-categories

Lorenzo Mantovani

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arXiv · 2105.02285

Localizations and completions of stable $\infty$-categories

Lorenzo Mantovani

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Abstract

We extend some classical results of Bousfield on homology localizations and nilpotent completions to a presentably symmetric monoidal stable $\infty$-category $\mathscr{M}$ admitting a multiplicative left-complete $t$-structure. If $E$ is a homotopy commutative algebra in $\mathscr{M}$ we show that $E$-nilpotent completion, $E$-localization, and a suitable formal completion agree on bounded below objects when $E$ satisfies some reasonable conditions.

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BibTeX RIS

Lorenzo Mantovani. 2021-05-05. Localizations and completions of stable $\infty$-categories. https://arxiv.org/abs/2105.02285

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