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Daniel Teixeira (Feb 18 2025 at 21:23):The definition of simplicial object valued in a bicategory can be weakened by asking the simplicial identities to hold up to coherent invertible 2-cells rather than strictly. These conveniently match pseudo-functors on .
This idea is not new, I recall seeing an article in the 90s (perhaps by Street) which worked the details out. Would anyone know what I'm talking about?
Mike Shulman (Feb 18 2025 at 23:09):Could you be thinking of "Fibrations in bicategories" (1980)?
David Kern (Feb 20 2025 at 01:14):While it's not written for general bicategories, this sounds like Corollary 1.6 of Jardine's Supercoherence.
Daniel Teixeira (Feb 20 2025 at 01:47):oh it was definitely this paper by Jardine! thanks Mike and David