Geodesic
Goodwillie calculus via adjunction and LS cocategory
Homology, homotopy, and applications, Tome 18 (2016) no. 2, pp. 31-58.

Voir la notice de l'article provenant de la source International Press of Boston

In this paper, we establish a new monadic structure on the intermediate constructions, $\mathrm{T}_n F$, of Goodwillie’s calculus of functors. We show that as a result these functors take values in spaces of Hopkins’ symmetric Lusternik–Schnirelmann (LS) cocategory $\leqslant n$, which is an upper bound on the homotopy nilpotence class of the space. This property allows us to extend results of Biedermann–Dwyer linking Goodwillie calculus to homotopy nilpotence and of Chorny–Scherer on the vanishing of Whitehead products for spaces which are values of $n$-excisive functors. We also use a dual form of our adjunction to give a rigorous formulation of homotopy functor analog of McCarthy’s Dual Calculus, where $n$-co-excisive functors take certain pullback cubes to pushout cubes, and dualize our results of calculus and LS cocategory to dual calculus and LS category.
DOI : 10.4310/HHA.2016.v18.n2.a2
Classification : 55P99, 55P45, 55Q15, 55U30
Keywords: LS category, LS cocategory, Goodwillie calculus, homotopy limit, nilpotence 
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     author = {Rosona Eldred},
     title = {Goodwillie calculus via adjunction and {LS} cocategory},
     journal = {Homology, homotopy, and applications},
     pages = {31--58},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n2.a2/}
}
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Rosona Eldred. Goodwillie calculus via adjunction and LS cocategory. Homology, homotopy, and applications, Tome 18 (2016) no. 2, pp. 31-58. doi : 10.4310/HHA.2016.v18.n2.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n2.a2/

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