GOODWILLIE CALCULUS VIA ADJUNCTION AND LS COCATEGORY.

In this paper, we establish a new monadic structure on the intermediate constructions, TnF, 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 ≤ 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. [ABSTRACT FROM AUTHOR]