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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 21st 2016
• (edited Mar 21st 2016)

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.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJul 17th 2018

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

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeJul 17th 2018

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

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJul 18th 2018

Thanks! I have added these pointers here.

• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeDec 30th 2018

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.