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 not deleted
user 42440
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.
7
votes
Quasicategories for non-simplicial model categories
You can consider the marked simplicial set $(N(\mathcal{C}),\mathcal{W})$, where $N$ is the usual nerve functor and $\mathcal{W}$ is the class of weak equivalences in your model category $\mathcal{C}$ …
- 1,354
3
votes
1
answer
351
views
Equivalent definition of a Kan fibration
It is known (follows for example from Proposition 4.2 of Simplicial Homotopy Theory by Goerss and Jardine) that a Kan-fibration can be defined as a map having the right lifting property with respect t …
- 1,354
7
votes
1
answer
183
views
Can a weak fibration category be non saturated?
A weak fibration category is a category $\mathcal{C}$ equipped with two subcategories
$$\mathcal{F}, \mathcal{W} \subseteq \mathcal{C}$$
containing all the isomorphisms, such that the following condit …
- 1,354
4
votes
$(\infty,1)$-categories and model categories
The functor $F$ you are looking for can be described as follows. Given a model category $M$, with class of weak equivalences $W$, one may associate to it an $\infty$-category $M_\infty$, equipped with …
- 1,354
8
votes
Accepted
Infinity category of functors from a relative category to a model category
The following is taken from Section 2.3.2 of
http://arxiv.org/abs/math/0207028
Let $C$ be a small simplicial category, $S\subseteq C$ a simplicial subcategory and $M$ a simplicial combinatorial mode …
- 1,354
12
votes
2
answers
649
views
Exponentiation in finite simplicial sets
A finite simplicial set is a simplicial set having only a finite number of non degenerate simplicies. My question is: if $A$ and $B$ are finite simplicial sets, does this imply that the simplicial set …
- 1,354
4
votes
1
answer
254
views
Is the simplicial set $(\Delta_3/\partial \Delta_3)^{\Delta_1}$ finite?
A simplicial set is called finite if it has only a finite number of non degenerate simplicies (or equivalently, if its number of $n$-simplicies grows polynomially with $n$). In an answer to a previou …
- 1,354
9
votes
Accepted
On combinatorial and cellular model categories and infinity categories
If you believe Vopěnka's principle then any cofibrantly generated model category is Quillen equivalent to a combinatorial one and thus its underlying $\infty$-category is presentable. It follows that …
- 1,354
2
votes
A fibrant-objects structure on Top
There was a mistake in an earlier version of the paper that you mention. If you define $\pi_0$-fibrations and $\pi_0$-equivalences the way that you did, they do not give the structure of a category o …
- 1,354
9
votes
0
answers
748
views
Standard model structures on $Top$
Call a model structure on $Top$ (the category of topological spaces) standard, if the weak equivalences are the weak homotopy equivalences. In this nLab page, two standard model structures on $Top$ ar …
- 1,354