Let $F,G: \mathcal{T}\to \mathcal{S}$ be two functors from topological spaces to spectra (or topological spaces) and let $s: F\to G$ be a morphism between them. Suppose $F$ and $G$ are analytic and we are given their Goodwillie towers. What can we say about $s$ in terms of the towers? Can we describe all morphisms between functors in terms of their towers?



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