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Sergey Arkhipov

Colored DG-operads and homotopy adjunction for DG-categories

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Colored DG-operads and homotopy adjunction for DG-categories. / Arkhipov, Sergey; Kanstrup, Tina.

2018.

Research output: Working paper/Preprint Working paperResearch

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@techreport{da33ad0317e24e7899eb8b2ce1e7e001,
title = "Colored DG-operads and homotopy adjunction for DG-categories",
abstract = " Generalizing the approach to pseudo monoidal DG-categories as certain colored non-symmetric DG-operads, we introduce a certain relaxed notion of a category enriched in DG-categories. We construct model structures on the category of colored non-symmetric DG-operads and on the category of DGCat-enriched categories with a fixed set of objects. This allows us to talk about strong homotopy maps in both settings. We discuss the notion of a strong homotopy monad in a DG-category and a notion of strong homotopy adjunction data for two DG-functors. ",
keywords = "math.CT",
author = "Sergey Arkhipov and Tina Kanstrup",
note = "Preliminary version, comments welcome! 28 pages",
year = "2018",
month = jun,
day = "26",
language = "English",
series = "arXiv",
type = "WorkingPaper",

}

RIS

TY - UNPB

T1 - Colored DG-operads and homotopy adjunction for DG-categories

AU - Arkhipov, Sergey

AU - Kanstrup, Tina

N1 - Preliminary version, comments welcome! 28 pages

PY - 2018/6/26

Y1 - 2018/6/26

N2 - Generalizing the approach to pseudo monoidal DG-categories as certain colored non-symmetric DG-operads, we introduce a certain relaxed notion of a category enriched in DG-categories. We construct model structures on the category of colored non-symmetric DG-operads and on the category of DGCat-enriched categories with a fixed set of objects. This allows us to talk about strong homotopy maps in both settings. We discuss the notion of a strong homotopy monad in a DG-category and a notion of strong homotopy adjunction data for two DG-functors.

AB - Generalizing the approach to pseudo monoidal DG-categories as certain colored non-symmetric DG-operads, we introduce a certain relaxed notion of a category enriched in DG-categories. We construct model structures on the category of colored non-symmetric DG-operads and on the category of DGCat-enriched categories with a fixed set of objects. This allows us to talk about strong homotopy maps in both settings. We discuss the notion of a strong homotopy monad in a DG-category and a notion of strong homotopy adjunction data for two DG-functors.

KW - math.CT

M3 - Working paper

T3 - arXiv

BT - Colored DG-operads and homotopy adjunction for DG-categories

ER -