---
date: 2022-04-05 23:42
modification date: Thursday 12th May 2022 16:53:16
title: "Goodwillie calculus"
aliases: [Goodwillie calculus]
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# Goodwillie calculus

Slogan: derivatives of the identity functor, $\partial_* I$, on a suitable model category should come equipped with a natural [operad](operad.md) structure. 

It is conjectured that in the category of algebras over a reduced operad $\mathcal{O}$ in spectra that the derivatives of the identity should be equivalent to $\mathcal{O}$ as operads. 

![](attachments/Pasted%20image%2020220519020129.png)