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Results tagged with stable-homotopy
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user 51164
Stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.
6
votes
Accepted
Spelling out explicitly the data of a two step filtration in terms of pieces and gluing data
Technically speaking the answer to your question is no, in the sense that the data of $(\alpha,\beta,\gamma,\delta)$ alone does not determine the filtered object $V_0 \subseteq V_1 \subseteq V_2$. How …
- 9,491
11
votes
1
answer
1k
views
The universal property of the unseparated derived category
In Appendix C of his book in progress Spectral Algebraic Geometry, Lurie defines the unseparated derived category $\check{{\cal D}}({\cal A})$ (see Definition C.5.8.2 loc.cit) associated to a Grothend …
- 17.9k
21
votes
Accepted
What's the stabilization of the $\infty$-category of $\infty$-categories?
In a project in progress with Matan Prasma and Joost Nuiten concerning the abstract cotangent complex formalism we compute the stabilization of the $\infty$-category $\infty\mathrm{Cat}_{/C}$ of $\inf …
- 9,491
2
votes
Accepted
Morphisms of parametrized ring spectra
So the answer is a bit surprising (maybe I have a mistake). You have an adjunction between $Fun(X,\mathrm{Sp})$ and $\mathrm{Sp}$ which in one direction sends a functor to its (homotopy) colimit and o …
- 9,491
9
votes
2
answers
1k
views
Genuine equivariant ambidexterity
A particular case of Lurie and Hopkins' ambidexterity theory is that if $G$ is a finite group acting on a $K(n)$-local spectrum $X$ then the norm map
$$ X_{hG} \to X^{hG} $$
is a $K(n)$-local equivale …
- 25.6k
4
votes
Accepted
Ambidexterity and Quantization
To my understanding the situation is roughly like this. Let $\mathcal{C}$ be an $\infty$-category admiting small limits and colimits and let $f: X \to Y$ be a map of spaces whose homotopy fiber is $n$ …
- 9,491