Timeline for The category theory of $(\infty, 1)$-categories
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2015 at 0:58 | answer | added | Tim Campion | timeline score: 13 | |
| Apr 12, 2013 at 7:11 | comment | added | Zhen Lin | @UrsSchreiber Thanks. Good to know that it's true in at least one pair of models! | |
| Apr 12, 2013 at 7:11 | comment | added | Zhen Lin | @DavidWhite I know about the Quillen equivalences, but how does that tell me what is happening to category-theoretic constructions inside the $(\infty, 1)$-categories? | |
| Apr 12, 2013 at 5:27 | comment | added | Urs Schreiber | Discussion of how Dwyer-Kan style homotopy theory in Kan-complex enriched categories relates to the notions in quasi-category theory is in appendix A.3.3 of Lurie "Higher Topos Theory". A quick survey is on the nLab here: ncatlab.org/nlab/show/homotopy+Kan+extension . | |
| Apr 12, 2013 at 2:18 | comment | added | David White | Are you aware of the work of Toen? Or the unicity theorem of Barwick and Schommer-Pries? They give axioms which any good model for $(\infty,n)$ homotopy theory should satisfy. Then they prove that all model are Quillen equivalent (and, even better, in a coherent way). In the introduction to the Unicity paper they talk a bit about why they chose to work in Quasi-categories (where the category-theoretic groundwork has been best laid), but comment that this could be done in any model. That suggests the answer to your question is Yes. | |
| Apr 11, 2013 at 8:55 | history | asked | Zhen Lin | CC BY-SA 3.0 |