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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

1. stub article for regular infinity categories

Anonymous

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 17th 2021

Thanks. I have just changed the “floating context menu” from “Higher category theory” to “$\infty$-Category theory”.

By the way, are you introducing the notion here, or should the page cite a reference?

• CommentRowNumber3.
• CommentAuthorHurkyl
• CommentTimeMay 17th 2021
• (edited May 17th 2021)

Huh. I would have thought you’d want to capture the notion of relation rather than the notion of epi-mono factorization.

That is, I would have generalized the notion as a finitely complete category with the property that groupoids are effective, and that pullbacks preserve geometric realizations (or maybe just geometric realizations of groupoids). I actually thought about creating such a stub myself.

Is there a relation between the two different ideas?

• CommentRowNumber4.
• CommentAuthorDavidRoberts
• CommentTimeMay 17th 2021

It’s not clear whether the $n$ in the definition is meant to vary over all $n\geq 0$, or if just one value of $n$ is needed.