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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?
Could you be thinking of "Fibrations in bicategories" (1980)?
While it's not written for general bicategories, this sounds like Corollary 1.6 of Jardine's Supercoherence.
oh it was definitely this paper by Jardine! thanks Mike and David