… homology groups of these derivatives. We also extend the bar construction to modules over
… naturally gives rise to a left module over the operad formed by the derivatives of the identity. …

… the symmetric sequence of Goodwillie derivatives of the identity functor on … a functor FM :
AlgO → AlgO at X ∈ AlgO by the simplicial bar construction … FM (X) = |Bar(M,O,X)| ≃ M ◦h O (X). …

… to spectra to understand the Goodwillie derivatives DnF of any … We assert that LFx(Sl) is
the bar construction on F(X), and … This allows us to identify H2(XAS}) with the bar construction …

… will play a role in the construction of higher derivatives. … construction in the sense of the
beginning of [Goo03, §1]. Use the Bousfield-Kan formulas or the two sided (co)bar construction to …

… Taylor tower and study the derivative through cross-effect and … as we deduce from it the
notion of derivatives ∂∗F, for any … This is a two sided bar construction on O when we consider …

… is a Quillen equivalence and furthermore the left derived functor Lf⇤ may be calculated
via a simplicial bar construction as follows (see, eg, [44]) Lf⇤(X) := O0 ◦h O(X) ' |Bar(O0, O,Xc)|. …

… The simplicial space UZMX is isomorphic to the "cyclic bar construction" on MX (cf. [16]). The
simplicial space U (X s' x A') is (… BMX is the bar construction on the topological monoid MX: …

… Taking this idea further one can also construct “module structures” over O for the derivatives
… saying that any O-algebra is canonically the (homotopical) realization of its bar construction. …

… Goodwillie towers of ∞-categories as described above. First we discuss the extra structure
present on the derivatives … This construction is closely related to Goodwillie’s construction of n-…

… In [7], Goodwillie constructs a universal n-excisive approximation PnF to a functor F. The …
Goodwillie shows that there is actually a functorial delooping of the derivative, so this …