Timeline for Free $2$-category on a $2$-quiver
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2022 at 19:24 | comment | added | Alec Rhea | @AlexanderCampbell This is indeed what I was looking for, thank you for the reference and thank you Mike for the link. If you'd like to post this as an answer I'll accept it to close out the question. | |
| Mar 12, 2022 at 23:50 | comment | added | Mike Shulman | Your description "the graph structure that underlies a 2-category" doesn't uniquely determine an answer. There is a free functor generating 2-categories from 2-globular sets, and also a free functor generated 2-categories from 2-computads, and other things in between. But I expect that computads (ncatlab.org/nlab/show/computad) are what you want. @AlexanderCampbell, I think you should post that as an answer. | |
| Mar 12, 2022 at 18:17 | comment | added | Alec Rhea | I’m looking for the ‘graph structure’ that ‘underlies a $2$-category’ in the same way that directed graphs underly ordinary categories. More precisely, there should be a forgetful functor from the $2$-category of $2$-categories to the $2$-category of ‘these structures’ whose left adjoint gives the ‘free $2$-category’ on one of ‘these structures’, categorifying one stage the fact that there is a forgetful functor from the $1$-category of categories to the $1$-category of directed graphs whose left adjoint gives the free category on a directed graph. | |
| Mar 12, 2022 at 8:50 | comment | added | Alexander Campbell | I believe Alec is after something like the more general concept of a (2-dimensional) computad (a.k.a. polygraph), introduced by Ross Street. | |
| Mar 12, 2022 at 8:12 | comment | added | Gjergji Zaimi | You could be looking for globular sets. 1-globular sets are precisely quivers. See here ncatlab.org/nlab/show/globular+set | |
| Mar 12, 2022 at 7:15 | history | asked | Alec Rhea | CC BY-SA 4.0 |