Bar and cobar constructions for curved algebras and coalgebras

V. V. Lyubashenko

We provide bar and cobar constructions as functors between some categories of curved algebras and curved augmented coalgebras over a graded commutative ring. These functors are adjoint to each other.

1. Yu. Bespalov, V.V. Lyubashenko, O. Manzyuk, Pretriangulated A1-categories, Proc. Inst. Math. NASU. Mathematics and its Applications, V.76, Institute of Mathematics of NAS of Ukraine, Kyiv, 2008.

2. Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono, Lagrangian intersection Floer theory: Anomaly and obstruction, AMS/IP Studies in Advanced Mathematics Series, V.46, Amer. Math. Soc., 2009.

3. V.V. Lyubashenko, A1-morphisms with several entries, arXiv:1205.6072, 2012.

4. A. Polishchuk, Introduction to curved dg-algebras, http://www.math.polytechnique.fr/SEDIGA/documents/ polishchuk_ens100324.pdf.

5. L. Positselski, Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence, Memoirs Amer. Math. Soc., 212 (2011), №996, vi+133, arXiv:0905.2621.

6. L. Positselski, Weakly curved A1-algebras over a topological local ring, 2012, arXiv:1202.2697.

	Bar and cobar constructions for curved algebras and coalgebras
Author	V. V. Lyubashenko lub@imath.kiev.ua Institute of Mathematics NASU
Abstract	We provide bar and cobar constructions as functors between some categories of curved algebras and curved augmented coalgebras over a graded commutative ring. These functors are adjoint to each other.
Keywords	curved algebra; curved augmented coalgebra; bar construction; cobar construction
Reference	1. Yu. Bespalov, V.V. Lyubashenko, O. Manzyuk, Pretriangulated A1-categories, Proc. Inst. Math. NASU. Mathematics and its Applications, V.76, Institute of Mathematics of NAS of Ukraine, Kyiv, 2008. 2. Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono, Lagrangian intersection Floer theory: Anomaly and obstruction, AMS/IP Studies in Advanced Mathematics Series, V.46, Amer. Math. Soc., 2009. 3. V.V. Lyubashenko, A1-morphisms with several entries, arXiv:1205.6072, 2012. 4. A. Polishchuk, Introduction to curved dg-algebras, http://www.math.polytechnique.fr/SEDIGA/documents/ polishchuk_ens100324.pdf. 5. L. Positselski, Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence, Memoirs Amer. Math. Soc., 212 (2011), №996, vi+133, arXiv:0905.2621. 6. L. Positselski, Weakly curved A1-algebras over a topological local ring, 2012, arXiv:1202.2697.
Pages	115-131
Volume	40
Issue	2
Year	2013
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html