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Results tagged with homotopy-theory
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user 51424
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
10
votes
Why do we care about $(\infty,2)$-categories?
One place where $(\infty,2)$-categories shows up is the geometric Langlands program. (As in David Ben-Zvi's comment, this is again related to the TFT example.) Indeed, local geometric Langlands is oft …
- 5,958
3
votes
Accepted
detecting weak equivalences in a simplicial model category II
I think the following gives a counterexample:
Take the category of morphisms in $\operatorname{SSet}$, i.e., the category $\operatorname{Fun}(C,\operatorname{SSet}),$ where $C$ is the category with t …
- 5,958
7
votes
1
answer
292
views
Proposition in HTT on cofibrations of categories
Proposition A.3.3.9. in Higher Topos Theory is as follows:
Let $S$ be an excellent model category and let $f:C\rightarrow C'$ be a cofibration of small $S$-enriched categories. Then (1) for every …
- 5,958