Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with homotopy-theory
Search options questions only
not deleted
user 144250
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.
4
votes
1
answer
225
views
The effect of straightening on morphisms
This is similar to another question on MO, but is different.
Let $p:\mathcal{E}\to\mathcal{C}$ be a right fibration between $\infty$-categories. As explained in Lurie's HTT, $\S$2.1, we can consider $ …
- 2,292
3
votes
1
answer
365
views
Homotopy coherent nerve versus simplicial nerve
Background
Recently I asked a question on a particular construction ot the classifying space of a topological group. I got an answer, but it relied on nontrivial Quillen equivalences between various m …
- 2,292
7
votes
2
answers
550
views
Simplicial nerve of a topological group
Given a group $G$, one way to construct the classifying (topological) space $BG$ is to regard $G$ as a category with one object and morphisms $G$, take its nerve, and then apply the geometric realizat …
- 2,292
8
votes
2
answers
578
views
Homotopic but not equivariantly homotopic maps
Let $G$ be a topological (or simplicial) group, let $X$ and $Y$ be $G$-spaces, and let $f,f':X\to Y$ be $G$-maps which are homotopic as maps of spaces. In general, $f$ and $f'$ may (of course) fail to …
- 2,292
6
votes
0
answers
302
views
Functorial identification of the mapping spaces of the arrow category of an $\infty$-category
Let $\mathcal{C}$ be a small $\infty$-category. Using the straightening-unstraightening construction, we can define a hom-functor of $\mathcal{C}$ as a functor $\mathcal{C}(-,-):\mathcal{C}^{\mathrm{o …
- 2,292
9
votes
2
answers
414
views
How do these definitions of factorization algebra compare?
Question
Several sources define (homotopy) factorization algebras in a seemingly
different manner (I am looking at [CG], [Gi], and
[CFM].) I wish to know how they compare with each other.
I apologize …
- 2,292
2
votes
1
answer
82
views
Reference request-Natural equivalence detected pointwise for complete Segal spaces
I am looking for a reference for the following elementary assertion on complete Segal spaces:
Let $A$ be a bisimplicial set and let $W$ be a complete Segal space. A morphism of $W^A$ is an equivalenc …
- 2,292
4
votes
1
answer
248
views
Why is the universal $n$-gerbe universal? (HTT, 7.2.2.26)
Let $\mathcal{X}$ be an $\infty$-topos and let $A$ be an abelian group object of the category $\operatorname{Disc}(\mathcal{X})$ of discrete objects of $X$. Recall that a morphism $f:\widetilde{X}\to …
- 2,292
6
votes
0
answers
133
views
Are cofibrant objects flat with respect to Day convolution?
Question
Let $\mathcal{C}$ be a small symmetric monoidal category. The category $\mathsf{sSet}^{\mathcal{C}}$ of simplicial precosheaves on $\mathcal{C}$ is a symmetric monoidal model category with r …
- 2,292