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I removed my recent material at simplex in a lined topos and instead inserted this now, expanded, at
where it belongs. There is now a section there that discusses how interval objects gives rise to cubical and simplicial path oo-categories.
The proposition I state there I have carefully checked. Should be correct. But haven't typed the proof, it doesn't lend itself to being typed (straightforward but tedious, as one says).
But if it is indeed correct, this must be standard well-known stuff. Does anyone have a reference?!
I also restructured and edited the rest of the entry a bit, trying to make it a bit nicer. THis entry deserves more attention, it is a pivotal entry.
Tomorrw when I am more awake I'll remove simplex in a lined topos and redirect links to it suitably to interval oject.
Last link: interval object
Added remark to interval object that the affine line A^1 is an interval object in the A^1 homotopy theory of schemes, but is obviously not like the interval in the topological sense.
Thanks David.
I had known about this from Zoran, but never looked into it in any detail.
But I have now at least picked up this thread and created stubs for
and
and linked to them from the paragraph that you added to interval object.
I also restructzred interval object a but further to amplify this point.
I also worked further on interval object:
expanded the introduction further, renames some headlines, added formal definition/theorem/proof environments, expanded the remarks on the meaning of the construction of that cosimplicial object.
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