Re: [HoTT] Quillen model structure

[Richard Williamson <rwilli...@gmail.com>]

Dear Thierry,

Forgive me for not quite having an overview of exactly what has
been done. My interest here is in how the model structure you
have constructed compares with Cisinski's work. For example, I
would expect that the category of cartesian cubical sets is a
test category. Indeed, I would expect that more or less exactly
the same technique as in 8.4 of Les préfaisceaux comme ... goes
through to prove this. And I would expect that one can put a
model structure on in the same way.

Now, I believe I saw in some slides that that your model
structure coincides with the Cisinski one. But this does not seem
compatible with my expectations above, because then it is
certainly Quillen equivalent to the Serre model structure on
topological spaces (or whatever).

Thus my questions:

1) Have I misinterpreted the slides or some other aspect of your
work?

2) If not, where exactly do Cisinski's techniques fail?

Best wishes,
Richard