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Gurkenglas (Jan 14 2022 at 13:45):I've now twice run into a "2-category" where a 2-cell a:f->g:S->T is an h with "forall s, h(f(s))<=h(g(s))". Is this an anti-pattern with a known do-this-instead? What's the closest thing to this that works?
Morgan Rogers (he/him) (Jan 14 2022 at 13:52):I was visiting the lab here in Paris for the first time yesterday and glanced at a poster in the corridor that was describing a 2-category which, if I'm recalling correctly, had 2-cells along those lines. Unfortunately none of the other content of the poster has stuck with me. If no one has replied by Monday when I next go into the lab, I'll tell you what the poster actually says :rolling_on_the_floor_laughing:
Paolo Perrone (Jan 14 2022 at 21:26):This reminds me of a coinserter, but I might be confused.
Morgan Rogers (he/him) (Jan 17 2022 at 08:34):Turns out the poster was talking about natural transformations between multimorphisms (i.e. I saw a pair of curved arrows and misremembered it as ), not what you were describing, sorry!