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Matteo Capucci (he/him) (Aug 19 2021 at 08:54):How do you call a 2-category which is actually a 1-category? I mean, everyone of its hom-cats is actually a set and composition is unital and associative on the nose
Fawzi Hreiki (Aug 19 2021 at 09:31):2-discrete?
Fawzi Hreiki (Aug 19 2021 at 09:32):Or perhaps 1-truncated.
David Michael Roberts (Aug 19 2021 at 09:32):Locally discrete?
Fawzi Hreiki (Aug 19 2021 at 09:36):That makes sense but then it becomes a pain for higher categories surely because you need to keep nesting the 'locally'
Reid Barton (Aug 19 2021 at 10:22):How about: a 1-category?
Jon Awbrey (Aug 19 2021 at 12:14):We often use the adjective degenerate in the case of other sorts of rankings.
Mike Shulman (Aug 19 2021 at 14:22):"Locally discrete" is the standard terminology for 2-categories. For generalizations to higher categories, one would go with something numerically indexed like "1-truncated".
Matteo Capucci (he/him) (Aug 19 2021 at 15:06):I'll go with 1-truncated, makes sense :)