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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 20th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexIn view of discussion in another thread ([here](https://nforum.ncatlab.org/discussion/7841/strom-model-structure/?Focus=95234#Comment_95234)), I have added ([here](https://ncatlab.org/nlab/show/Parametrized+Homotopy+Theory#Subtleties)) the following warning: *** Beware that section 4.4 claims a new proof of the [[Strøm model structure]], but relying on a statement in * [[Michael Cole]], *Many homotopy categories are homotopy categories*, Topology and its Applications 153 (2006) 1084–1099 ([doi:10.1016/j.topol.2005.02.006](https://doi.org/10.1016/j.topol.2005.02.006)) which later was noticed to be false, by [[Richard Williamson]], for details see p. 2 and Rem 5.12 and Sec. 6.1 in: * [[Tobias Barthel]], [[Emily Riehl]], _On the construction of functorial factorizations for model categories_, Algebr. Geom. Topol. 13 (2013) 1089-1124 ([arXiv:1204.5427](http://arxiv.org/abs/1204.5427), [doi:10.2140/agt.2013.13.1089](http://dx.doi.org/10.2140/agt.2013.13.1089), [euclid:agt/1513715550](https://projecteuclid.org/euclid.agt/1513715550)) *** It remains unclear, to me anyways, what this implies for the sliced generalization which is the core claim of May & Sigurdsson's book.(?) <a href="https://ncatlab.org/nlab/revision/diff/Parametrized+Homotopy+Theory/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/Parametrized+Homotopy+Theory/10">v10</a>, <a href="https://ncatlab.org/nlab/show/Parametrized+Homotopy+Theory">current</a>

   In view of discussion in another thread (here), I have added (here) the following warning:

   ---

   Beware that section 4.4 claims a new proof of the Strøm model structure, but relying on a statement in

   • Michael Cole, Many homotopy categories are homotopy categories, Topology and its Applications 153 (2006) 1084–1099 (doi:10.1016/j.topol.2005.02.006)

   which later was noticed to be false, by Richard Williamson, for details see p. 2 and Rem 5.12 and Sec. 6.1 in:

   • Tobias Barthel, Emily Riehl, On the construction of functorial factorizations for model categories, Algebr. Geom. Topol. 13 (2013) 1089-1124 (arXiv:1204.5427, doi:10.2140/agt.2013.13.1089, euclid:agt/1513715550)

   ---

   It remains unclear, to me anyways, what this implies for the sliced generalization which is the core claim of May & Sigurdsson’s book.(?)

   diff, v10, current