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• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeJan 30th 2015
• (edited Jan 30th 2015)

I see Urs added to synthetic geometry

That the line does not consist of points, nor the plane of lines, follows from their concepts (PdN§256b).

I wonder if it’s time to add something to point. As it stands there’s nothing of the cohesive points, such as the superpoint. We have infinitesimally thickened point linking in both directions to superpoint, so I can add some links to these from point. But I guess we could say something more in the text.

In view of our discussion over here, in particular

Of course I don’t know what happens for various flavours of tangent cohesion, these might well have immensely rich tiny objects, since the spectra over the point in tangent cohesion are infinitesimal,

it seems not so easy to read off points from their cohesive contexts. Is it really so difficult to say what points are for a specific tangent $\infty$-topos? If we took $T(Smooth \infty Grpd)$, so smooth parameterized spectra, aren’t points just $\mathbb{R}^{(0|E)}$, indexed by a spectrum $E$?

One thing I’m not sure about is when to treat points of a kind together, as in superpoints of all degrees forming a category, and when individually, if that’s what’s happening at the root of the brane bouquet.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeFeb 1st 2015

True, somebody should try to find time to add something.

Maybe I should first think more about how to phrase precisely the idea of points in relative cohesion. It’s something like a generator in the base topos.

My battery is dying right now. I’ll try to think of something better to put in the entry…