Operads and chain rules for the calculus of functors

Arone, Greg ; Ching, Michael

Astérisque, no. 338 (2011) , 168 p.

MR Zbl

@book{AST_2011__338__1_0,
     author = {Arone, Greg and Ching, Michael},
     title = {Operads and chain rules for the calculus of functors},
     series = {Ast\'erisque},
     year = {2011},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {338},
     mrnumber = {2840569},
     zbl = {1239.55004},
     language = {en},
     url = {https://www.numdam.org/item/AST_2011__338__1_0/}
}

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AU  - Arone, Greg
AU  - Ching, Michael
TI  - Operads and chain rules for the calculus of functors
T3  - Astérisque
PY  - 2011
IS  - 338
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_2011__338__1_0/
LA  - en
ID  - AST_2011__338__1_0
ER  -

%0 Book
%A Arone, Greg
%A Ching, Michael
%T Operads and chain rules for the calculus of functors
%S Astérisque
%D 2011
%N 338
%I Société mathématique de France
%U https://www.numdam.org/item/AST_2011__338__1_0/
%G en
%F AST_2011__338__1_0

Arone, Greg; Ching, Michael. Operads and chain rules for the calculus of functors. Astérisque, no. 338 (2011), 168 p. https://www.numdam.org/item/AST_2011__338__1_0/

Bibliographie
Cité par

[1] G. Arone - "A generalization of Snaith-type filtration", Trans. Amer. Math. Soc. 351 (1999), p. 1123-1150. | MR | Zbl | DOI

[2] G. Arone, "The Weiss derivatives of $B O (-)$ and $B U (-)$ ", Topology 41 (2002), p. 451-481. | MR | Zbl

[3] G. Arone, "Derivatives of the embedding functor II : the unstable case", in preparation.

[4] G. Arone & M. Kankaanrinta - "A functorial model for iterated Snaith splitting with applications to calculus of functors", Fields Inst. Commun. 19 (1998), p. 1-30. | MR | Zbl

[5] G. Arone & M. Mahowald - "The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres", Invent. Math. 135 (1999), p. 743-788. | MR | Zbl | DOI

[6] M. Basterra & M. A. Mandell - "Homology and cohomology of $E_{\infty}$ ring spectra", Math. Z. 249 (2005), p. 903-944. | MR | Zbl | DOI

[7] C. Berger & I. Moerdijk - "Axiomatic homotopy theory for operads", Comment. Math. Helv. 78 (2003), p. 805-831. | MR | Zbl | DOI

[8] A. K. Bousfield & D. M. Kan - Homotopy limits, completions and localizations, Lecture Notes in Math., vol. 304, Springer, 1972. | MR | Zbl

[9] M. Ching - "Bar constructions for topological operads and the Goodwillie derivatives of the identity", Geom. Topol. 9 (2005), p. 833-933. | MR | Zbl | EuDML | DOI

[10] M. Ching, "A chain rule for Goodwillie derivatives of functors from spectra to spectra", Trans. Amer. Math. Soc. 362 (2010), p. 399-426. | MR | Zbl | DOI

[11] M. Ching, "A note on the composition product of symmetric sequences in a symmetric monoidal category", arXiv:math.CT/0510490. | Zbl

[12] J. D. Christensen & D. C. Isaksen - "Duality and pro-spectra", Algebr. Geom. Topol. 4 (2004), p. 781-812. | MR | Zbl | EuDML | DOI

[13] A. D. Elmendorf, I. Kriz, M. A. Mandell & J. P. May - Rings, modules, and algebras in stable homotopy theory, Mathematical Surveys and Monographs, vol. 47, Amer. Math. Soc., 1997. | MR | Zbl

[14] V. Ginzburg & M. Kapranov - "Koszul duality for operads", Duke Math. J. 76 (1994), p. 203-272. | MR | Zbl | DOI

[15] P. G. Goerss & J. F. Jardine - Simplicial homotopy theory, Progress in Math., vol. 174, Birkhäuser, 1999. | MR | Zbl

[16] T. G. Goodwillie - "Calculus. I. The first derivative of pseudoisotopy theory", K-Theory 4 (1990), p. 1-27. | MR | Zbl | DOI

[17] T. G. Goodwillie, "Calculus. II. Analytic functors", K-Theory 5 (1991/92), p. 295-332. | MR | Zbl | DOI

[18] T. G. Goodwillie, "Calculus. III. Taylor series", Geom. Topol. 7 (2003), p. 645-711. | MR | Zbl | EuDML | DOI

[19] J. P. C. Greenlees & J. P. May - "Generalized Tate cohomology", Mem. Amer. Math. Soc. 113 (1995). | MR | Zbl

[20] J. E. Harper - "Homotopy theory of modules over operads in symmetric spectra", Algebr. Geom. Topol. 9 (2009), p. 1637-1680. | MR | Zbl | DOI

[21] V. Hinich - "Homological algebra of homotopy algebras", Comm. Algebra 25 (1997), p. 3291-3323. | MR | Zbl | DOI

[22] P. S. Hirschhorn - Model categories and their localizations, Mathematical Surveys and Monographs, vol. 99, Amer. Math. Soc. 2003. | MR | Zbl

[23] M. Hovey - Model categories, Mathematical Surveys and Monographs, vol. 63, Amer. Math. Soc. 1999. | MR | Zbl

[24] D. C. Isaksen - "Calculating limits and colimits in pro-categories", Fund. Math. 175 (2002), p. 175-194. | MR | Zbl | EuDML | DOI

[25] W. P. Johnson - "The curious history of Faa di Bruno's formula", Amer. Math. Monthly 109 (2002), p. 217-234. | MR | Zbl

[26] G. M. Kelly - "Basic concepts of enriched category theory", Repr. Theory Appl. Categ. 10 (2005). | MR | Zbl

[27] J. R. Klein & J. Rognes - "A chain rule in the calculus of homotopy functors", Geom. Topol. 6 (2002), p. 853-887. | MR | Zbl | EuDML | DOI

[28] T. A. Kro - "Model structure on operads in orthogonal spectra", Homology, Homotopy Appl. 9 (2007), p. 397-412. | MR | DOI

[29] N. J. Kuhn - "Tate cohomology and periodic localization of polynomial functors", Invent Math. 157 (2004), p. 345-370. | MR | Zbl | DOI

[30] N. J. Kuhn, "Goodwillie towers and chromatic homotopy: an overview", in Proceedings of the Nishida Fest (Kinosaki 2003), Geom. Topol. Monogr., vol. 10, Geom. Topol. Publ., Coventry, 2007, p. 245-279. | MR | Zbl

[31] L. G. J. Lewis - "Is there a convenient category of spectra?", J. Pure Appl. Algebra 73 (1991), p. 233-246. | MR | Zbl | DOI

[32] L. G. J. Lewis, J. P. May, M. Steinberger & J. E. Mcclure - Equivariant stable homotopy theory, Lecture Notes in Math., vol. 1213, Springer, 1986. | MR | Zbl

[33] J. Lurie - Higher topos theory, Annals of Math. Studies, vol. 170, Princeton Univ. Press, 2009. | MR | Zbl

[34] J. Lurie, " $(\infty, 2)$ -categories and the Goodwillie calculus I", preprint arXiv:0905.0462.

[35] S. Maclane - Categories for the working mathematician, Graduate Texts in Math., vol. 5, Springer, 1971. | MR | Zbl

[36] M. A. Mandell, J. P. May, S. Schwede & B. E. Shipley - "Model categories of diagram spectra", Proc. London Math. Soc. 82 (2001), p. 441-512. | MR | Zbl | DOI

[37] M. Markl, S. Shnider & J. Stasheff - Operads in algebra, topology and physics, Mathematical Surveys and Monographs, vol. 96, Amer. Math. Soc., 2002. | MR | Zbl

[38] J. P. May - The geometry of iterated loop spaces, Lectures Notes in Mathematics, vol. 271, Springer, 1972. | MR | Zbl

[39] J. P. May & J. Sigurdsson - Parametrized homotopy theory, Mathematical Surveys and Monographs, vol. 132, Amer. Math. Soc., 2006. | MR | Zbl | DOI

[40] R. Mccarthy - "Dual calculus for functors to spectra", in Homotopy methods in algebraic topology (Boulder, CO, 1999), Contemp. Math., vol. 271, Amer. Math. Soc., 2001, p. 183-215. | MR | Zbl | DOI

[41] C. W. Rezk - "Spaces of algebra structures and cohomology of operads", Ph.D. Thesis, Massachusetts Institute of Technology, 1996. | MR

[42] S. Schwede - " $S$ -modules and symmetric spectra", Math. Ann. 319 (2001), p. 517-532. | MR | Zbl | DOI

[43] S. Schwede & B. E. Shipley - "Algebras and modules in monoidal model categories", Proc. London Math. Soc. 80 (2000), p. 491-511. | MR | Zbl | DOI

[44] S. Schwede & B. E. Shipley, "Stable model categories are categories of modules", Topology 42 (2003), p. 103-153. | MR | Zbl | DOI

[45] Spitzweck - "Operads, algebras and modules in general model categories", preprint arXiv.math/0101102. | Zbl

[46] M. Weiss - "Orthogonal calculus", Trans. Amer. Math. Soc. 347 (1995), p. 3743-3796. | MR | Zbl | DOI