A note on a Holstein construction

Arkhipov, Sergey; Poliakova, Daria

doi:10.4310/hha.2020.v22.n2.a9

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Homotopy Limits In Dg-categories1

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2021

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“…We obtain such a functor from Holstein, Poliakova and Arkhipov: 4.0.1. Theorem (Holstein 2016, section 3 andPoliakova 2018).…”

Section: Homotopy Limits In Dg-categoriesmentioning

confidence: 99%

Homotopy limits in the category of dg-categories in terms of $$ \mathrm {A}_{\infty } $$-comodules

Arkhipov

Ørsted

2021

European Journal of Mathematics

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In this paper, we apply an explicit construction of a simplicial powering in dg-categories, due to Holstein (2016) and Arkhipov and Poliakova (2018), as well as our own results on homotopy ends (Arkhipov and Ørsted 2018), to obtain an explicit model for the homotopy limit of a cosimplicial system of dg-categories. We apply this to obtain a model for homotopy descent in terms of A ∞-comodules, proving a conjecture by Block, Holstein, and Wei (2017) in the process.

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“…We obtain such a functor from Holstein, Poliakova and Arkhipov: 4.0.1. Theorem (Holstein 2016, section 3 andPoliakova 2018).…”

Section: Homotopy Limits In Dg-categoriesmentioning

confidence: 99%

Homotopy limits in the category of dg-categories in terms of $$ \mathrm {A}_{\infty } $$-comodules

Arkhipov

Ørsted

2021

European Journal of Mathematics

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A note on a Holstein construction

Abstract: We clarify details and fill certain gaps in the construction of a canonical Reedy fibrant resolution for a constant simplicial DGcategory due to Holstein.

Cited by 1 publication

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Homotopy limits in the category of dg-categories in terms of $$ \mathrm {A}_{\infty } $$-comodules

Homotopy limits in the category of dg-categories in terms of $$ \mathrm {A}_{\infty } $$-comodules

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