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Does the naive/genuine distinction correspond to anything from a linear HoTT perspective?
Yes, genuine $G$-spectra are equivalently the motives of fractional 0-branes. Only that people usually say “spectral Mackey functor”, in order not to give away what it really means ;-)
Reading fractional D-brane I can kinda see what you mean, and something like this has been building up with that talk of motives of G-sets (which I now can’t find) and the Burnside category. Is it written out on some page?
I see I was led to a similar question as #2 a couple of years ago. Push-pull through correspondences are everywhere.
Thanks for reminding me of the pointer to that old discussion. So I am referring to my old comment just beneath yours there.
For a long time I thought that it must be a meaningless coincidence that $G$-spectra realized as spectral Mackey functors are the 1d cohomological quantum field theory of a funny kind of G-particles. Now maybe, in view of equivariant stable cohomotopy classification of M-brane charge, I am beginning to see how it all comes together. Something like a spectral BFSS model for fractional 0-branes.
What does “whose degrees of freedom are a set of 9+1 large matrices” mean at BFSS model? There are 10 matrices of a large size?
like this:
$$
\begin{aligned}
A &= B
\\
C &= D
\end{aligned}
$$
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