Category of A∞-categories

Homology, Homotopy and Applications

Volumn 5, Issue 1, 2003, Pages 1-48

  Lyubashenko, Volodymyr ^a  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

2 category; A transformations; A categories; A functors; Unit A transformation

Indexed keywords

EID: 18544370869     PISSN: 15320073     EISSN: 15320081     Source Type: Journal    
DOI: 10.4310/HHA.2003.v5.n1.a1     Document Type: Article

References (27)

1. [Bat98] M. A. Batanin, Monoidal globular categories as natural environment for the theory of weak n-categories, Adv. Math. 136 (1998), 39-103.
2. [Boa66] J. M. Boardman, The principle of signs, Enseignement Math. (2) 12 (1966), 191-194.
3. [Bou73] N. Bourbaki, Univers, SGA 4: Théorie des Topos et Cohomologie Etale des Schémas, Tome 1. Théorie des Topos, Lect. Notes in Math., vol. 269, Springer, Heidelberg, 1972-1973, appendice, pp. 185-217.
4. [Car48] H. Cartan, Sur la cohomologie des espaces où opère un groupe. Notions algébriques préliminaires, C. R. Acad. Sci. Paris 226 (1948), no. 2, 148-150.
5. [Dri02] V. G. Drinfeld, DG quotients of DG categories, math.KT/0210114, 2002.
6. [FOOO] K. Fukaya, Y.-G. Oh, H. Ohta, and K. Ono, Lagrangian intersection Floer theory - anomaly and obstruction - , book in preparation.
7. [Fuk] K. Fukaya, Floer homology and mirror symmetry II, preprint.
8. ∞-category, and Floer homologies, The Proceedings of the 1993 GARC Workshop on Geometry and Topology (H. J. Kim, ed.), Lecture Notes series, vol. 18, Seoul National University, 1993, 1-102.
9. ∞-algebras and the cyclic bar complex, Illinois J. Math. 34 (1990), no. 2, 256-283.
10. [Gri87] P.-P. Grivel, Catégories dérivées et fondeurs dérivés, Algebraic D-modules (J. Coates and S. Helgason, eds.), Perspectives in Mathematics, vol. 2, Academic Press, Boston, New York, London, Tokyo, 1987, pp. 1-108.
11. [GV73] A. Grothendieck and J. L. Verdier, Préfaisceaux, SGA 4: Théorie des Topos et Cohomologie Etale des Schémas, Tome 1. Théorie des Topos, Lect. Notes in Math., vol. 269, Springer, Heidelberg, 1972-1973, pp. 1-184.
12. [Kad80] T. V. Kadeishvili, On the theory of homology of fiber spaces, Uspekhi Mat. Nauk 35 (1980), no. 3, 183-188,
13. Translated in Russ. Math. Surv. 35 (1980) no. 3, 231-238.
14. [Kad82] T. V. Kadeishvili, The algebraic structure in the homology of an A(∞)-algebra, Soobshch. Akad. Nauk Gruzin. SSR 108 (1982), no. 2, 249-252, in Russian.
15. [Kel01] B. Keller, Introduction to A-infinity algebras and modules, Homology, Homotopy and Applications 3 (2001), no. 1, 1-35.
16. [Kel82] G. M. Kelly, Basic concepts of enriched category theory, London Math. Soc. Lecture Notes, vol. 64, Cambridge Univ. Press, Cambridge, 1982.
17. [KL01] T. Kerler and V. V. Lyubashenko, Non-semisimple topological quantum field theories for 3-manifolds with corners, Lect. Notes in Math., vol. 1765, Springer-Verlag, Heidelberg, 2001, vi+379 p.
18. [Kon95] M. Kontsevich, Homological algebra of mirror symmetry, Proc. Internat. Cong. Math., Zürich, Switzerland 1994 (Basel), vol. 1, Birkhäuser Verlag, 1995, 120-139.
19. ∞-categories and non-commutative geometry, in preparation, 2002.
20. [KS] M. Kontsevich and Yan Soibelman, Deformation theory, book in preparation.
21. [Kos47] J.-L. Koszul, Sur les opérateurs de dérivation dans un anneau, C. R. Acad. Sci. Paris 225 (1947), 217-219.
22. ∞- catégories, Ph.D. thesis, in preparation, 2002.
23. [Lei02] T. Leinster, A survey of definitions of n-category, Theory Appl. Categ. 10 (2002), 1-70 (electronic).
24. [Mac63] S. Mac Lane, Homology, Die Grundlehren der mathematischen Wissenschaften, no. 114, Springer-Verlag, Berlin, Heidelberg, 1963.
25. [Smi80] V. A. Smirnov, Homology of fiber spaces, Uspekhi Mat. Nauk 35 (1980), no. 3, 227-230 ,
26. Translated in Russ. Math. Surveys 35 (1980) no 3, 294-298.
27. [Sta63] J. D. Stasheff, Homotopy associativity of H-spaces, I & II, Trans. Amer. Math. Soc. 108 (1963), 275-292, 293-312.