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Daniel Teixeira (Nov 09 2023 at 01:02):I'm having a hard time finding a definition of normal homomorphism in Lack's papers. What is it? A pseudofunctor that preserves identities strictly? Why do we need that to get a bicat of bicats with icons as 2-morphisms?
Daniel Teixeira (Nov 09 2023 at 01:07):well it seems that you can put virtually anything as 1-morphisms and still get a 2-category
image.png
(from the Johnson-Yau book)
Kevin Arlin (Nov 09 2023 at 01:27):I bet you haven't actually seen a claim by Lack that normality of homomorphisms is relevant to constructing a 2-category of bicategories, since he's the one who fully introduced icons and the original paper barely mentions normal homomorphisms. But yes, they're the strictly unital pseudofunctors.
Daniel Teixeira (Nov 09 2023 at 01:29):yeah, you're right. I think I was asking this because I first saw icons in his paper with Paoli, where it is the normal morphisms that are taken as 1-morphisms