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Josh Chen (Jul 31 2024 at 14:25):This feels folkloric, but is there some written proof of the analogue of the pullback pasting lemma for pseudo-pullbacks? I'm writing up the equivalent version for wild pullbacks and would like to relate it to existing literature. Thanks!
Kevin Carlson (Jul 31 2024 at 17:15):The nlab page on comma objects gives a pasting lemma, but with no reference. It's probably the kind of thing most people writing on 2-category theory will have tended to leave to the reader. https://ncatlab.org/nlab/show/comma+object
Josh Chen (Aug 01 2024 at 10:32):Thanks! I expected so but it's always good to ask experts...
Kevin Carlson (Aug 01 2024 at 17:57):As long as we're here, maybe it's worth noting that pseudo-pullbacks and iso-commas are equivalent but not isomorphic, in general, while the frequently important lax pullbacks and commas are not equivalent at all. It's easy to mix them up.