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Keywords:
Functor calculus
Functor calculus
Summary:
We study versions of Goodwillie’s calculus of functors for indexing diagrams other than cubes. We in particular construct universal excisive approximations for a larger class of diagrams, which yields an extension of the Taylor tower. We prove that the limit of this extension agrees with the limit of the Taylor tower using criteria for the existence of maps between excisive approximations. Lastly we investigate in which cases our new notions of excision coincide with classical ones.
References:
[1] Arone, Gregory, Ching, Michael: Goodwillie calculus. Handbook of homotopy theory, pages , MR 4197981
[2] Ayoub, Joseph: Les six opérations de grothendieck et le formalisme des cycles évanescents dans le monde motivique. i. Astérisque, Vol. 314 MR 2423375
[3] Davey, B. A., Priestley, H. A.: Introduction to lattices and order. Cambridge University Press, DOI:10.1017/CBO9780511809088 DOI 10.1017/CBO9780511809088 | MR 1902334
[4] Goodwillie, Thomas G.: Calculus i: The first derivative of pseudoisotopy theory. K-Theory, Vol. 4, Iss. 1, 1-27, DOI:10.1007/BF00534191 DOI 10.1007/BF00534191
[5] Goodwillie, Thomas G.: Calculus II: Analytic functors. K-Theory, Vol. 5, Iss. 4, 295-332, DOI:10.1007/BF00535644 DOI 10.1007/BF00535644
[6] Goodwillie, Thomas G.: Calculus III: Taylor series. Geometry & Topology, Vol. 7, 645-711, https://arxiv.org/abs/math/0310481, DOI:10.2140/gt.2003.7.645 DOI 10.2140/gt.2003.7.645 | MR 2026544
[7] Groth, Moritz, Ponto, Kate, Shulman, Michael: Mayer-vietoris sequences in stable derivators. Homology, Homotopy and Applications, Vol. 16, Iss. 1, 265-294, https://arxiv.org/abs/1306.2072, DOI:10.4310/HHA.2014.v16.n1.a15 DOI 10.4310/HHA.2014.v16.n1.a15 | MR 3211746
[8] Kelly, G. M., Street, Ross: Review of the elements of 2-categories. Category seminar. Proceedings sydney category theory seminar 1972/1973, pp 75-103, DOI:10.1007/BFb0063101 DOI 10.1007/BFb0063101
[9] Kuhn, Nicholas J.: Goodwillie towers and chromatic homotopy: An overview. Proceedings of the nishida fest (kinosaki 2003), pp 245-279, DOI:10.2140/gtm.2007.10.245 DOI 10.2140/gtm.2007.10.245 | MR 2402789
[10] Lurie, Jacob: Higher topos theory. Annals of mathematics studies 170, Princeton University Press, https://arxiv.org/abs/math/0608040 MR 2522659
[11] Lurie, Jacob: Higher algebra. http://www.math.harvard.edu/~lurie/papers/HA.pdf
[12] Lurie, Jacob: Kerodon. https://kerodon.net
[13] May, J. P.: A concise course in algebraic topology. Chicago lectures in mathematics, University of Chicago Press
[14] Pereira, Luís Alexandre: A general context for goodwillie calculus. https://arxiv.org/abs/1301.2832
[15] Rezk, Charles: A streamlined proof of goodwillie’s n–excisive approximation. Algebraic & Geometric Topology, Vol. 13, 1049-1051, https://arxiv.org/abs/0812.1324, DOI:10.2140/agt.2013.13.1049 DOI 10.2140/agt.2013.13.1049 | MR 3044601
[16] Riehl, Emily, Verity, Dominic: The 2-category theory of quasi-categories. Advances in Mathematics, Vol. 280, 549-642, https://arxiv.org/abs/1306.5144, DOI:10.1016/j.aim.2015.04.021 DOI 10.1016/j.aim.2015.04.021 | MR 3350229
[17] Riehl, Emily, Verity, Dominic: Elements of \infty-category theory. Cambridge studies in advanced mathematics 194, Cambridge University Press, DOI:10.1017/9781108936880 DOI 10.1017/9781108936880 | MR 4354541
[18] Stoll, Robin: A version of goodwillie calculus for non-cubes. Master’s Thesis, Universität Bonn
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