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Colored DG-operads and homotopy adjunction for DG-categories

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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.
Original languageEnglish
Publication statusPublished - 26 Jun 2018
SeriesarXiv

Bibliographical note

Preliminary version, comments welcome! 28 pages

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