Timeline for $(\infty,n)$ categories as fibrant objects in a model “space”
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 20 at 17:19 | comment | added | Tim Campion | Every model of $(\infty,n)$-category that I'm aware of arises as the fibrant objects of a model structure on some complete and cocomplete 1-category. That's usually the way the model is defined. This includes the case $n=\infty$. Many of these models are discussed in Barwick and Schommer-Pries, the most notable exception being Verity's complicial model. | |
| Oct 18 at 14:10 | comment | added | Simon Henry | You'll find a general overview on theta spaces and lots of references here : ncatlab.org/nlab/show/Theta-space in short they are a generalisation of Segal spaces that provide a model for $(\infty,n)$-categories. | |
| Oct 18 at 2:22 | comment | added | Pinak Banerjee | @SimonHenry Could you briefly elaborate a bit on your comment, especially \theta spaces? Apologies for lack of background. | |
| Oct 17 at 13:09 | comment | added | Simon Henry | Segal spaces are another model for $(\infty,1)$-category, this time using simplicial spaces instead of simplicial sets ( so bi-simplicial sets). Not a model of $(\infty,n)$ or $(\infty,\infty)$. They are however easier to generalise to $(\infty,n)$ or $(\infty,\infty)$ than quasicategories (using either $\Theta$-spaces, or iterated Segal spaces). | |
| Oct 17 at 6:24 | history | edited | Andrej Bauer | CC BY-SA 4.0 |
added 3 characters in body; edited title
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| Oct 17 at 6:22 | comment | added | David Roberts♦ | See eg Ara's Higher quasi-categories vs higher Rezk spaces arxiv.org/abs/1206.4354 or Barwick's (∞, n)-Cat as a closed model category proquest.com/docview/305445747 | |
| Oct 17 at 6:02 | history | edited | Martin Sleziak |
added a top-level tag; https://meta.mathoverflow.net/questions/1457/why-are-mo-tags-formatted-as-they-are
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| Oct 17 at 5:59 | history | asked | Pinak Banerjee | CC BY-SA 4.0 |