From: Thierry Coquand <Thierry...@cse.gu.se>
To: homotopy Type Theory <homotopyt...@googlegroups.com>
Subject: trivial cofibration-fibration factorization
Date: Thu, 6 Jul 2017 20:09:57 +0000 [thread overview]
Message-ID: <D2DF99DA-1BF9-4A5A-B0EA-5316B5E04E10@chalmers.se> (raw)
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For completeness, I wrote down the details <http://www.cse.chalmers.se/~coquand/afs.pdf> of the trivial cofibration-fibration
factorisation in the cubical set model.
It is interesting to compare this with the “small object argument”.
There is no quotient operations and the argument can instead
be seen as an inductive process which is similar to Petersson-Synek “tree types”
(a.k.a. indexed containers): we define inductively a family of sets indexed by
the object of the base category (and all operations are then defined by induction
of this inductively defined indexed family of sets).
Thierry
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