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Goodwillie calculus is a way of understanding a functor $F$ in terms of its Goodwillie tower, a tower whose limit approximates $F$, whose layers can be understood in terms of stable data. Derived deformation theory is a way of understanding objects $c$ of an $\infty$-category via a tower whose limit approximates $c$, and whose layers can be understood in terms of stable data.

Question: What is the relationship, more precisely, between Goodwillie calculus and derived deformation theory? For instance, is one a special case of the other?

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    $\begingroup$ At best, they might be instances of the same phenomenon, as are Postnikov towers. The key to DDT is that every square-zero extension can in a sense be delooped - see e.g. section 3.2 of arxiv.org/abs/2109.14594 . $\endgroup$
    – Jon Pridham
    Commented Oct 19, 2022 at 19:58
  • $\begingroup$ Sorry to interrupt, would you have a short remark on how Goodwillie tower should be understood as Postnikov towers? $\endgroup$
    – Yang
    Commented Sep 11 at 2:34

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