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[84.202.247.109]) by smtp.gmail.com with ESMTPSA id l25-v6sm1107991ljj.30.2018.06.14.13.15.04 (version=TLS1_2 cipher=ECDHE-RSA-CHACHA20-POLY1305 bits=256/256); Thu, 14 Jun 2018 13:15:05 -0700 (PDT) Date: Thu, 14 Jun 2018 22:15:03 +0200 From: Richard Williamson To: Steve Awodey Cc: Thierry Coquand , Homotopy Theory Subject: Re: [HoTT] Quillen model structure Message-ID: <20180614201503.GA1968@richard.richard> References: <20180614183959.GA1401@richard.richard> <54A8E26C-ECF8-441A-AC3F-7643DA47C3FE@cmu.edu> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Disposition: inline Content-Transfer-Encoding: 8bit In-Reply-To: <54A8E26C-ECF8-441A-AC3F-7643DA47C3FE@cmu.edu> User-Agent: Mutt/1.9.5 (2018-04-13) Dear Steve and Thierry, > I believe the answer to (1) is yes : - ) Hehe, that is very likely, and I will be happy to acknowledge it! :-) > Where exactly this conflicts with a Cisinski style approach is > a distinct issue, I think — maybe that’s your (2)? Exactly. It has been a little while since I was really working on this stuff, so I could be forgetting something, but as far as I know the test model structure on cartesian cubical sets is exactly the one coming from the theorem of Cisinski that Thierry cites using the obvious cylinder, and with empty S. Now, Thierry also says, I believe, that this model structure is the same as the one of Christian Sattler. How can this be?! Presumably I have something wrong, but I do not see yet what it is after the replies so far. Best wishes, Richard