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I added a reference to globular set.
I have edited globular set a little, trying to prettyfie the exposition mainly. Also added another line or two to the Idea-section and added another reference.
Is anything known about globular sets in terms of Grothendieck homotopy theory? For instance, is the category of globes a weak test category, a test category, or a strict test category?
I’m pretty sure it is provably not a test category. Just now I’m not sure of a reference, I’ll see if I can remember one later.
That’s what I thought I remembered too, but I don’t know the reference either. My intuition is that the boundary of a globular set is “too simple to encode composition” the way (say) simplices and cubes do.
This is discussed in Scholie 8.4.14 in Cisinski’s Astérisque 308.
Something is seriously broken on the nLab. It appears that new edits edit the second-to-the-last version instead of the latest one!
What exactly does this article mean by this sentence:
They are one of the major geometric shapes for higher structures: if they satisfy a globular Segal condition then they are equivalent to strict ∞-categories.
What is the “globular Segal condition”? I thought we need to pass from the category of globes to the category Theta_n to formulate such a Segal condition?
(Added by Urs on November 6, 2012 in Revision 24.)
Thanks for highlighting. That sentence didn’t make good sense. I have replaced it by:
Globular sets have been used as a geometric shape for higher structures: when equipped with suitable composition operation on their cells they model a notion of strict ∞-categories.
I have further expanded that sentence on relation to models for higher catgeories, adding pointer also to associative n-categories.
And so I now gave the paragraph its own subsection: “Properties – As shapes for higher categories” (now here).
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