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Title
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Filtered cA∞-categories and functor categories
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Author
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Abstract
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| We develop the basic theory of curved A1-categories (cA1- categories) in a ltered setting, encompassing the frameworks of Fukaya categories [5] and weakly curved A1-categories in the sense of Positselski [17]. Between two cA1-categories a and b, we introduce a cA1-category qFun(a; b) of so-called qA1-functors in which the uncurved objects are precisely the cA1-functors from a to b. The more general qA1-functors allow us to consider representable modules, a feature which is lost if one restricts attention to cA1-functors. We formulate a version of the Yoneda Lemma which shows every cA1-category to be homotopy equivalent to a curved dg category, in analogy with the uncurved situation. We also present a curved version of the bar-cobar adjunction. |
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Language
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English
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Source (journal)
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Applied categorical structures. - Dordrecht, 1993, currens
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Publication
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Dordrecht
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2018
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ISSN
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0927-2852
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DOI
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10.1007/S10485-018-9526-2
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Volume/pages
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26
:5
(2018)
, p. 943-996
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ISI
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000445266900010
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Full text (Publisher's DOI)
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Full text (open access)
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Full text (publisher's version - intranet only)
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