Algebraic & Geometric Topology Volume 9, issue 3 (2009)

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Homotopy theory of modules over operads in symmetric spectra

John E Harper

Algebraic & Geometric Topology 9 (2009) 1637–1680

DOI: 10.2140/agt.2009.9.1637

Bibliography

1	M Basterra, M A Mandell, Homology and cohomology of $E_\infty$ ring spectra, Math. Z. 249 (2005) 903 MR2126222
2	C Berger, I Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003) 805 MR2016697
3	W Chachólski, J Scherer, Homotopy theory of diagrams, Mem. Amer. Math. Soc. 155 (2002) MR1879153
4	W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
5	A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Math. Surveys and Monogr. 47, Amer. Math. Soc. (1997) MR1417719
6	A D Elmendorf, M A Mandell, Rings, modules, and algebras in infinite loop space theory, Adv. Math. 205 (2006) 163 MR2254311
7	B Fresse, Lie theory of formal groups over an operad, J. Algebra 202 (1998) 455 MR1617616
8	B Fresse, Koszul duality of operads and homology of partition posets, from: "Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic $K$–theory" (editors P G Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 115 MR2066499
9	B Fresse, Modules over operads and functors, Lecture Notes in Math. 1967, Springer (2009) MR2494775
10	E Getzler, J D S Jones, Operads, homotopy algebra and iterated integrals for double loop spaces arXiv:hep-th/9403055v1
11	V Ginzburg, M Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994) 203 MR1301191
12	P G Goerss, M J Hopkins, André–Quillen (co)-homology for simplicial algebras over simplicial operads, from: "Une dégustation topologique [Topological morsels]: homotopy theory in the Swiss Alps (Arolla, 1999)" (editors D Arlettaz, K Hess), Contemp. Math. 265, Amer. Math. Soc. (2000) 41 MR1803952
13	P G Goerss, M J Hopkins, Moduli spaces of commutative ring spectra, from: "Structured ring spectra" (editors A Baker, B Richter), London Math. Soc. Lecture Note Ser. 315, Cambridge Univ. Press (2004) 151 MR2125040
14	P G Goerss, M J Hopkins, Moduli problems for structured ring spectra (2005)
15	P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Math. 174, Birkhäuser Verlag (1999) MR1711612
16	J E Harper, Homotopy theory of modules over operads and non-$\Sigma$ operads in monoidal model categories arXiv:0801.0191
17	V Hinich, Homological algebra of homotopy algebras, Comm. Algebra 25 (1997) 3291 MR1465117
18	V Hinich, V Schechtman, Homotopy Lie algebras, from: "I M Gel$'$fand Seminar" (editors S Gel′fand, S Gindikin), Adv. Soviet Math. 16, Amer. Math. Soc. (1993) 1 MR1237833
19	P S Hirschhorn, Model categories and their localizations, Math. Surveys and Monogr. 99, Amer. Math. Soc. (2003) MR1944041
20	M Hovey, Model categories, Math. Surveys and Monogr. 63, Amer. Math. Soc. (1999) MR1650134
21	M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
22	M Kapranov, Y Manin, Modules and Morita theorem for operads, Amer. J. Math. 123 (2001) 811 MR1854112
23	G M Kelly, On the operads of J P May, Repr. Theory Appl. Categ. (2005) 1 MR2177746
24	I Kříž, J P May, Operads, algebras, modules and motives, Astérisque (1995) MR1361938
25	L G Lewis Jr., M A Mandell, Modules in monoidal model categories, J. Pure Appl. Algebra 210 (2007) 395 MR2320005
26	S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1998) MR1712872
27	M A Mandell, $E_\infty$ algebras and $p$–adic homotopy theory, Topology 40 (2001) 43 MR1791268
28	M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. $(3)$ 82 (2001) 441 MR1806878
29	M Markl, S Shnider, J Stasheff, Operads in algebra, topology and physics, Math. Surveys and Monogr. 96, Amer. Math. Soc. (2002) MR1898414
30	J P May, The geometry of iterated loop spaces, Lectures Notes in Math. 271, Springer (1972) MR0420610
31	J E McClure, J H Smith, A solution of Deligne's Hochschild cohomology conjecture, from: "Recent progress in homotopy theory (Baltimore, MD, 2000)" (editors D M Davis, J Morava, G Nishida, W S Wilson, N Yagita), Contemp. Math. 293, Amer. Math. Soc. (2002) 153 MR1890736
32	J E McClure, J H Smith, Operads and cosimplicial objects: an introduction, from: "Axiomatic, enriched and motivic homotopy theory" (editor J P C Greenless), NATO Sci. Ser. II Math. Phys. Chem. 131, Kluwer Acad. Publ. (2004) 133 MR2061854
33	D G Quillen, Homotopical algebra, Lecture Notes in Math. 43, Springer (1967) MR0223432
34	D G Quillen, Rational homotopy theory, Ann. of Math. $(2)$ 90 (1969) 205 MR0258031
35	C Rezk, Spaces of algebra structures and cohomology of operads, PhD thesis, Massachusetts Institute of Technology (1996)
36	S Schwede, $S$–modules and symmetric spectra, Math. Ann. 319 (2001) 517 MR1819881
37	S Schwede, An untitled book project about symmetric spectra (2007)
38	S Schwede, B Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. $(3)$ 80 (2000) 491 MR1734325
39	B Shipley, A convenient model category for commutative ring spectra, from: "Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic $K$–theory" (editors P G Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 473 MR2066511
40	V A Smirnov, Homotopy theory of coalgebras, Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985) 1302, 1343 MR816858
41	M Spitzweck, Operads, algebras and modules in general model categories arXiv:math/0101102v1