Publication
Title
Filtered cA∞-categories and functor categories
Author
Abstract
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.
Language
English
Source (journal)
Applied categorical structures. - Dordrecht, 1993, currens
Publication
Dordrecht : 2018
ISSN
0927-2852
Volume/pages
26:5(2018), p. 943-996
ISI
000445266900010
Full text (Publisher's DOI)
Full text (open access)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 08.05.2018
Last edited 28.08.2021
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