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Stream: learning: reading & references

Topic: "weak" simplicial objects


view this post on Zulip Daniel Teixeira (Feb 18 2025 at 21:23):

The definition of simplicial object valued in a bicategory B\mathcal B 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 Δop\Delta^{op}.

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?

view this post on Zulip Mike Shulman (Feb 18 2025 at 23:09):

Could you be thinking of "Fibrations in bicategories" (1980)?

view this post on Zulip 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.

view this post on Zulip Daniel Teixeira (Feb 20 2025 at 01:47):

oh it was definitely this paper by Jardine! thanks Mike and David