Timeline for Weakening simplicial identities
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 26, 2014 at 20:24 | comment | added | Mike Shulman | Yes, that is also a good reference! | |
| Apr 26, 2014 at 16:19 | comment | added | Dimitri Chikhladze | Now I discovered that Steve Lack's "Codescent objects and coherence, JPAA 175 (2002), 223–241" has some things about the lax situation. | |
| Apr 26, 2014 at 15:57 | vote | accept | Dimitri Chikhladze | ||
| Apr 26, 2014 at 10:35 | comment | added | Dimitri Chikhladze | Yes, that is more like what I meant. In particular I was wondering about the lax version of "descent theory". | |
| Apr 26, 2014 at 3:13 | comment | added | Mike Shulman | I realized later that there is a possible different answer to your second question, which might be more like what you had in mind. Namely, there are two more 2-categories $\Delta^\dagger$ and $\Delta^\diamond$, which have the analogous relationships to lax monads and oplax monads. They exist for formal reasons, but to my knowledge no one has studied them carefully or proven a coherence theorem. These really do "replace the simplicial identities by noninvertible 2-cells", whereas Todd's $\Delta$ keeps the simplicial identities as equalites and adds additional noninvertible 2-cells. | |
| Apr 25, 2014 at 23:26 | comment | added | Dimitri Chikhladze | Thanks to both of you. I"ll take a look at these things. | |
| Apr 25, 2014 at 20:26 | history | answered | Mike Shulman | CC BY-SA 3.0 |