Timeline for Higher categories using just simplicial sets
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 21 at 18:38 | comment | added | Daniel Bruegmann | @DanielTeixeira Yes, complicial sets are simplicial sets with extra structure. I am asking if the forgetful functor is faithful when restricted to a certain subcategory, which I am open to changing. | |
| Sep 20, 2023 at 15:04 | comment | added | Daniel Teixeira | I don't know what's the current status of the theory, but didn't Riehl's complicial sets project precisely model (oo,n)-categories as simplicial sets with structure? | |
| Sep 16, 2023 at 22:29 | comment | added | Simon Henry | Interesting! In any case, it is known that Street Nerve (from strict infinity category to simplicial sets) is not fuly faitfull (but it become fuly faithfull when viewed as valued in complicial sets with the appropriate notion of thiness. I don't quite remember what is the counter-exemple, but I'd expect it would provide also a negative answer to your question... So the answer might be in old paper of Street and/or Roberts... but I haven't been able to find it. | |
| Sep 16, 2023 at 19:29 | comment | added | Daniel Bruegmann | @SimonHenry First question: yes (see kerodon.net/tag/01W9) Second question: I don't know. | |
| Sep 16, 2023 at 19:11 | comment | added | Simon Henry | Wait, Is it true for $n=2$? | |
| Sep 16, 2023 at 16:32 | history | asked | Daniel Bruegmann | CC BY-SA 4.0 |