Questions tagged [calculus-of-functors]

Calculus of functors is a tool for studying functors between categories, analogous to the Taylor expansion of a real-valued function. It was originated by Thomas Goodwillie for studying spaces of concordances / pseudo-isotopy embeddings.

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29
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3answers
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Surveys of Goodwillie Calculus

Is there a good general introduction to Goodwillie calculus out there, like a paper or publication that gives a general overview of the calculus as well as how it is useful and why we are interested ...
25
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2answers
1k views

Seeing stacks in the Calculus of Functors

Recently I was told (by an algebraic geometer) that when algebraic geometers look at the Calculus of Functors, they think of stacks. When I look at the Calculus of Functors, I see a categorification ...
6
votes
4answers
670 views

A reference for Calculus of Functors for Model Categories

I am wondering where I might look to see what has been done in terms of Calculus of Functors for more general weak equivalences and Model Categories. I am at least aware of some of the extended ...
5
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0answers
185 views

Homotopy functor calculus vs functor calculus in additive categories

Consider the Goodwillie calculus of a homotopy functor $F : \mathrm{Sp} \to \mathrm{Sp}$, where $\mathrm{Sp}$ denotes an appropriate model for spectra (... orthogonal spectra for instance). Then ...
1
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1answer
125 views

Calculus of Functors and Model categories

In Calculus of functors and model categories II Biedermann and Rondigs claim in Corollary 6.18 that the $n$-homogeneous model structure on $\mathrm{Fun}(\mathcal{C}, \mathcal{D})$ is stable if $\...
-1
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1answer
57 views

A question on decreasing function [closed]

Let $t\in (0,1)$ and ${a_n}{x^n} + .... + {a_1}{x^1} + f(t) = 0$ $f(t) $ is continuous decreasing function of $t$. $a_i\ge0$ for all $i$. $y(t)$ is positive real zero of the first equition. Can we ...