# Filtered $$cA_\infty$$ c A ∞ -Categories and Functor Categories

Filtered $$cA_\infty$$ c A ∞ -Categories and Functor Categories Appl Categor Struct https://doi.org/10.1007/s10485-018-9526-2 Filtered cA -Categories and Functor Categories 1 1,2 Olivier De Deken · Wendy Lowen Received: 29 December 2017 / Accepted: 24 April 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract We develop the basic theory of curved A -categories (cA -categories) in a ﬁl- ∞ ∞ tered setting, encompassing the frameworks of Fukaya categories (Fukaya et al. in Part I, AMS/IP studies in advanced mathematics, vol 46, American Mathematical Society, Provi- dence, RI, 2009) and weakly curved A -categories in the sense of Positselski (Weakly curved A algebras over a topological local ring, 2012. arxiv:1202.2697v3). Between two cA - ∞ ∞ categories a and b, we introduce a cA -category qFun(a, b) of so-called qA -functors in ∞ ∞ which the uncurved objects are precisely the cA -functors from a to b. The more general qA -functors allow us to consider representable modules, a feature which is lost if one To Bob Lowen: The distance, ever changing Between the one and the other The drop and the ocean The hill and the mountain top The distance, ever smaller Between many and one Life and love Now and forever Communicated by Ross http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Categorical Structures Springer Journals

# Filtered $$cA_\infty$$ c A ∞ -Categories and Functor Categories

, Volume OnlineFirst – May 28, 2018
54 pages

/lp/springer_journal/filtered-ca-infty-c-a-categories-and-functor-categories-xChuLX1imh
Publisher
Springer Netherlands
Subject
Mathematics; Mathematical Logic and Foundations; Theory of Computation; Convex and Discrete Geometry; Geometry
ISSN
0927-2852
eISSN
1572-9095
D.O.I.
10.1007/s10485-018-9526-2
Publisher site
See Article on Publisher Site

### Abstract

Appl Categor Struct https://doi.org/10.1007/s10485-018-9526-2 Filtered cA -Categories and Functor Categories 1 1,2 Olivier De Deken · Wendy Lowen Received: 29 December 2017 / Accepted: 24 April 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract We develop the basic theory of curved A -categories (cA -categories) in a ﬁl- ∞ ∞ tered setting, encompassing the frameworks of Fukaya categories (Fukaya et al. in Part I, AMS/IP studies in advanced mathematics, vol 46, American Mathematical Society, Provi- dence, RI, 2009) and weakly curved A -categories in the sense of Positselski (Weakly curved A algebras over a topological local ring, 2012. arxiv:1202.2697v3). Between two cA - ∞ ∞ categories a and b, we introduce a cA -category qFun(a, b) of so-called qA -functors in ∞ ∞ which the uncurved objects are precisely the cA -functors from a to b. The more general qA -functors allow us to consider representable modules, a feature which is lost if one To Bob Lowen: The distance, ever changing Between the one and the other The drop and the ocean The hill and the mountain top The distance, ever smaller Between many and one Life and love Now and forever Communicated by Ross

### Journal

Applied Categorical StructuresSpringer Journals

Published: May 28, 2018

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