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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 21st 2016
   • (edited Mar 21st 2016)
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   Author: Urs
   Format: MarkdownItexI gave _[[functorial factorization]]_ its own little entry, for ease of pointing to the precise definition. This is for the moment just copied over from the corresponding paragraph at _[[weak factorization system]]_ (where I have re-organized the sectzion outline slightly, for clarity). Also I added cross-links with some relevant entries.

   I gave functorial factorization its own little entry, for ease of pointing to the precise definition.

   This is for the moment just copied over from the corresponding paragraph at weak factorization system (where I have re-organized the sectzion outline slightly, for clarity). Also I added cross-links with some relevant entries.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJul 17th 2018
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   Author: Urs
   Format: MarkdownItexIn a simplicial model category with small object argument. Can functorial factorization be _simplicially_ functorial?

   In a simplicial model category with small object argument. Can functorial factorization be simplicially functorial?

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeJul 17th 2018
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   Author: Mike Shulman
   Format: MarkdownItexYes, because every simplicial set is cofibrant. See 4.3.8 in Hirschhorn's book or 24.2 [here](https://arxiv.org/abs/math/0610194).

   Yes, because every simplicial set is cofibrant. See 4.3.8 in Hirschhorn’s book or 24.2 here.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 18th 2018
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   Author: Urs
   Format: MarkdownItexThanks! I have added these pointers [here](https://ncatlab.org/nlab/show/functorial+factorization#Properties).

   Thanks! I have added these pointers here.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeDec 30th 2018
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   Author: Mike Shulman
   Format: MarkdownItexRemoved references to wfs (not all functorial factorizations are wfs's), moved the explicit definition into the definition section alongside the abstract definition, and added the equivalence to pointed endofunctors over cod. <a href="https://ncatlab.org/nlab/revision/diff/functorial+factorization/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/functorial+factorization/5">v5</a>, <a href="https://ncatlab.org/nlab/show/functorial+factorization">current</a>

   Removed references to wfs (not all functorial factorizations are wfs’s), moved the explicit definition into the definition section alongside the abstract definition, and added the equivalence to pointed endofunctors over cod.

   diff, v5, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMay 14th 2023
   • (edited May 14th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Daniel Dugger]], Prop. 7.1 in: *Combinatorial model categories have presentations*, Advances in Mathematics **164** 1 (2001) 177-201 &lbrack;[arXiv:math/0007068](https://arxiv.org/abs/math/0007068), [doi:10.1006/aima.2001.2015](https://doi.org/10.1006/aima.2001.2015)&rbrack; * [[Clark Barwick]], Prop. 2.5 in: *On left and right model categories and left and right Bousfield localizations*, Homology, Homotopy and Applications **12** 2 (2010) 245–320 &lbrack;[doi:10.4310/hha.2010.v12.n2.a9](https://doi.org/10.4310/hha.2010.v12.n2.a9), [euclid:1296223884](https://projecteuclid.org/journals/homology-homotopy-and-applications/volume-12/issue-2/On-left-and-right-model-categories-and-left-and-right/hha/1296223884.full), subsuming: [arXiv:0708.2067](https://arxiv.org/abs/0708.2067), [arXiv:0708.2832](https://arxiv.org/abs/0708.2832), [arXiv:0708.3435](http://arxiv.org/abs/0708.3435)&rbrack; as references for functorial factorization in combinatorial model categories, and made this an Example-item ([here](https://ncatlab.org/nlab/show/functorial+factorization#InCombinatorialModelCategories)) <a href="https://ncatlab.org/nlab/revision/diff/functorial+factorization/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/functorial+factorization/7">v7</a>, <a href="https://ncatlab.org/nlab/show/functorial+factorization">current</a>

   added pointer to:

   • Daniel Dugger, Prop. 7.1 in: Combinatorial model categories have presentations, Advances in Mathematics 164 1 (2001) 177-201 [arXiv:math/0007068, doi:10.1006/aima.2001.2015]

   • Clark Barwick, Prop. 2.5 in: On left and right model categories and left and right Bousfield localizations, Homology, Homotopy and Applications 12 2 (2010) 245–320 [doi:10.4310/hha.2010.v12.n2.a9, euclid:1296223884, subsuming: arXiv:0708.2067, arXiv:0708.2832, arXiv:0708.3435]

   as references for functorial factorization in combinatorial model categories, and made this an Example-item (here)

   diff, v7, current