Timeline for Grothendieck's Homotopy Hypothesis - Applications and Generalizations
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 20, 2014 at 11:37 | answer | added | Ronnie Brown | timeline score: 11 | |
| Jun 14, 2014 at 16:52 | vote | accept | CommunityBot | moved from User.Id=62675 by developer User.Id=36770 | |
| Jun 14, 2014 at 16:52 | vote | accept | CommunityBot | moved from User.Id=62675 by developer User.Id=36770 | |
| Jun 14, 2014 at 16:52 | |||||
| Jun 14, 2014 at 13:42 | vote | accept | CommunityBot | moved from User.Id=62675 by developer User.Id=36770 | |
| Jun 14, 2014 at 16:52 | |||||
| Jun 13, 2014 at 22:59 | answer | added | D.-C. Cisinski | timeline score: 36 | |
| Jun 13, 2014 at 14:32 | answer | added | Todd Trimble | timeline score: 32 | |
| Jun 13, 2014 at 11:49 | comment | added | Todd Trimble | @PhilippeGaucher Grothendieck does discuss that sort of dislike in his Esquisse d'un Programme, where he wants a formalism of tamely stratified spaces. | |
| Jun 13, 2014 at 11:49 | comment | added | S. Carnahan♦ | As far as "why is this fundamental?" is concerned, topological spaces are fundamental objects in mathematics, and groupoids are also very important, so it is natural that people are interested in a strong relation between them. On the other hand, the answer to any "can this be generalized" question is "yes". | |
| Jun 13, 2014 at 10:37 | comment | added | Philippe Gaucher | @Charles Rezk I believe that Grothendieck did not like the notion of topological space and wanted a "purely algebraic" representation of homotopy types. Though I cannot remember where I read that. | |
| Jun 13, 2014 at 1:35 | comment | added | Charles Rezk | My question would be: why did Grothendieck care? I assume it is because he wanted a general (and generalized) theory of stacks, but i don't actually know. | |
| Jun 13, 2014 at 1:18 | comment | added | user62675 | @ZhenLin Also, can it be generalized? That is the question which I'm more interested in. | |
| Jun 13, 2014 at 1:15 | comment | added | user62675 | @ZhenLin I know that $(\infty,n)$-categories can be interpreted in terms of homotopy theory as $n$-fold complete Segal spaces. Are there any more fundamental applications, e.g., to homotopy type theory? | |
| Jun 13, 2014 at 1:10 | comment | added | Zhen Lin | An important application of this hypothesis is the elimination of the notion of $\infty$-groupoid: since we do not know how to define the latter, we may as well define it to be a homotopy type (of a CW complex). This shortcut then lets us define $(\infty, 1)$-categories in terms of homotopy theory. | |
| Jun 12, 2014 at 22:56 | history | asked | user62675 | CC BY-SA 3.0 |