12:16 AM
I know geometric realization commutes with finite products, but I don't know of a counterexample for the case of arbitrary products. Does anyone have a good one on hand?

2 hours later…
2:09 AM
@LPK The Hilbert cube does not admit the structure of a CW complex, so most infinite products are counterexamples.

5 hours later…
6:51 AM
@LPK See Jacob Lurie's comment here: mathoverflow.net/questions/181188/…

13 hours later…
7:49 PM
As far as I understand there are quite a few rigorous graphical languages for tensor calculations. Does anyone know why none of them are as widely spread as say ordinary category theory? Or even string diagrams.
There are without a doubt some areas (i'm thinking specifically in differential geometry but not only) where tensor calculations can become quite heavy
I'm thinking in particular of the fact that when you have a huge contraction of tensors in rimannian geometry most of the indices are irrelevant. I'm pretty sure one can replace the whole contraption with a graph together with an order on the edges coming and going into each vertex plus a decoration of vertices by tensors. Does anyone know of such a graphical language?

There's Penrose diagrams but these are much more general and not quite what i'm looking for. In particular i'm looking for a graphical language which uses the fact that there's a non-degenerate linear form to simplify the no

8:54 PM
I can't really think of a place that pictorial representation of tensors would simplify a calculation substantially. Replacing a bunch of contracted indices with a graph doesn't seem like a big save of energy.

9:53 PM
is there an analogue of nagata compactification in the derived and/or spectral setting?
i'm reading brian conrad's paper on the classical theorem, and the proof seems to be very geometric
i would hazard the guess that the answer is probably "no", because if you could do something like this (for stacks) then the construction of Tmf from TMF would come basically for free