8 problems

Let $C$ be the category appearing above, let $L{\mathsf{Sp}}$ be the corresponding localized category of spectra, and write $\partial^{BB}_\ast$ for the Goodwillie derivative funct…

Bimodule chain-rule conjecture. For functors

Mixed chain-rule conjecture. There is an equivalence of right $K(\mathsf{OEpi})$-modules

Let $X$ be a space and let $n>2$. Define $LS_2(X)\leq n-2$ when $X$ has Lusternik–Schnirelmann category at most $n$ and admits an open cover $U_1,\ldots,U_n$ such that each map…

Let $n$ be a nonnegative integer, let $\mathcal{P}^n$ be a theory in the sense of Lawvere, and let its objects be the free homotopy conilpotent groups of class $n$, namely products…

Dual Goodwillie calculus conjecture. There should be a cooperad $\partial_*(\Sigma^\infty_\mathcal{C}\Omega^\infty_\mathcal{C})$ and an equivalence of operads

Let $E_r^{k,t}(S^1)$ denote the pages of the Goodwillie spectral sequence (GSS) for $S^1$. Goodwillie–Whitehead conjecture, weak form. The GSS for $S^1$ collapses at the $E_2$-page…

For each $k$, let … be the map in Kuhn's Kahn–Priddy sequence, and let … be the $k$-invariant map of the Goodwillie tower for $S^1$. Goodwillie–Whitehead conjecture, strong form. ……