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Thomas's guest post at cafe and his paper should maybe be reflected in entry infinity-category and other places in nlab where various "models" fro infinity categories are listed, as it should have a very important role in my opinion, but still better experts should do carefully these changes. I might give a slightly uninformed interepretation of the role of this work in comparison to the experts like Mike.
I suspect that Thomas’s models are free not only in the sense that he ascribes to them. For instance, [[simplicial T-complex]]es would seem to form a ‘variety’ in his category of algebraic Kan complexes where the equations satisfied are the three axioms of those beasties.
To help a bit to see how Thomas’s work fits into the general framework, I have been doing a bit of maintenance work on [[simplicial T-complexes]] and [[crossed complexes]], including mention of the nerve of a crossed complex.
Thanks, Tim.
Could one maybe add a remark about results about simplicial T-complexes? We have the definition, and, as you amplify, it is more restrcitve than just saying that for every horn a filler has been chosen. So it would be good to understand what the extra conditions accomplish. What is it they allow to prove? Or generally, what did people in the literature accomplish or try to accomplish with simplicial T-complexes.
Remarks on questions like this might be good at simplicial T-complex.
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