Re: [HoTT] A unifying cartesian cubical type theory

[Thomas Streicher <streicher@mathematik.tu-darmstadt.de>]

> Maybe one can expect them never to coincide, by the following loose
> reasoning: in between the minimal model structure and the test model
> structure should lie something like an (infinity,1)-model structure,
> i.e. something like a cubical version (in the chosen flavour) of a
> quasi-categorical model structure, and one does not of course expect
> the (infinity,1)-model structure to coincide with the test one. For
> simplicial sets it is known of course that one has the
> quasi-categorical model structure strictly lying in between the
> minimal one and the test one.

but in simplicial sets the minimal and the test model structure do
coincide (since filling open boxes is tantamount to filling horns as
shown at the beginning of Goerss and Jardine)

Thomas

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