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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2009

    added the general definition to cofibrantly generated model category

    (that entry still deserves more attention, though...)

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 23rd 2009

    added to cofibrantly generated model category the statement and proof of Kan's "recognition theorem" under Properties.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 24th 2009

    removed from cofibrantly generated model category the extra section on presentable ones, which became superfluous after Mike (if I saw correctly) added the clause that generating cofibrations and acyclic cofibrations admit the small object aregument.

    Instead, I moved now the statement that  cof(I) = llp(rpl(I)) below the main definition and supplied the details of the proof

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 15th 2012

    Started at cofibrantly generated model category a section Presentation and generation with some statement. To be expanded.

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeJul 21st 2013

    Does anyone have a reference for non-cofibrantly generation of pro-space (and more generally pro-model category) model structures? Boris Chorny makes reference to this in one of his papers, but I cannot find the comment in the referred paper (at least on the version I have of it).

    It seems that pro-spaces have a fibrantly generated model structure on the other hand. Again does any one know good references for such (other than taking the dual of a cofib one)? These would seem to be important in some of the motivic contexts, but I quickly get out of my depth there. I am needing this for the profinite homotopy stuff that I am writing but will eventually put more on the Lab.

    • CommentRowNumber6.
    • CommentAuthorZhen Lin
    • CommentTimeJul 21st 2013

    Perhaps you’re thinking of Isaksen [2001], A model structure on the category of pro-simplicial sets? There it is remarked that the factorisations are not even functorial – so it’s neither fibrantly nor cofibrantly generated. (To be clear, what is proved (§ 19) is that it is not cofibrantly generated; but Isaksen says that factorisations are not functorial either.)

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeJul 21st 2013
    • (edited Jul 21st 2013)

    Thanks, Zhen Lin. I checked my preprint copy and found no section 19. I must have an earlier version. I will look for the newer version. (I have found the TAMS version on my hard disc, so fine, and again thanks.)

    • CommentRowNumber8.
    • CommentAuthorTim_Porter
    • CommentTimeJul 22nd 2013

    Actually, the proof of factorisation suffers from the inadequacy of language. Isaaksen shows that there is a factorisation but does not claim that it is functorial. in the process he says it is non-functorial' rather than sayingfunctoriality is not claimed’ or similar. This looks a bit like an example of the red herring principle in disguise!

    These interactions between the set theory used for setting up pro-sSet and the small object argument intrigue me. Does anyone have any ‘wisdom’ to enlighten me? (Note it seems that pro-sSet may be fibrantly generated!)

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