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Shea Levy (Oct 22 2020 at 16:47):Is there any effort toward systematizing names of various constructions (maybe similar to IUPAC's rules for chemical compounds)?
In particular, I have a structure where 1-cells have a list of 0-cells as their domain and codomain, 2-cells have a single 1-cell for their domain and codomain, and 1-cell composition is only lax associative. What do I call this?
Nathanael Arkor (Oct 22 2020 at 17:39):Maybe a "lax poly-bicategory".
Nathanael Arkor (Oct 22 2020 at 17:39):There's also "lax bipolycategory", but I associate this more strongly with the idea of also having polycategorical 2-cells.
Amar Hadzihasanovic (Oct 22 2020 at 20:45):Alas, poly-bicategory has already been used by Cockett, Koslowski and Seely for what maybe should have rather been called a "coloured polycategory", that is, what stands in relation to polycategories the way that bicategories stand to monoidal categories.
Paolo Perrone (Oct 22 2020 at 21:14):A IUPAC-style naming convention would be good.
Amar Hadzihasanovic (Oct 23 2020 at 09:07):IUPAC style here would probably be something like (2,lax)-(1,poly)-bicategory
Amar Hadzihasanovic (Oct 23 2020 at 09:09):Or rather 2-category : I suspect IUPAC would set the standard to be weak.
Shea Levy (Oct 23 2020 at 09:15):Not weak FYI, lax. We have a two-cell from e.g. to , but it's not necessarily invertible.
Shea Levy (Oct 23 2020 at 09:16):(I may not be using that terminology correctly :sweat_smile: )