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Stream: practice: terminology & notation

Topic: What is ICat?

Bryce Clarke (Nov 22 2024 at 13:21):

I am reading the paper Double fibrations. Throughout the paper, they make use of a (2-)category $\mathbf{ICat}$, however I cannot seem to find where it is defined. I could certainly guess what it, based on the generalised version in Definition 3.24. Is this standard notation?

Bryce Clarke (Nov 22 2024 at 13:23):

My assumption is that the objects are pseudo-functors $\mathbf{C}^{\mathrm{op}} \rightarrow \mathbf{Cat}$ from a category $\mathbf{C}$, i.e. an [[indexed category]].

Mike Shulman (Nov 22 2024 at 15:43):

Yes, I think that's what they mean.

Mike Shulman (Nov 22 2024 at 15:44):

I wouldn't say it's standard notation.