Timeline for How canonical is cofibrant replacement?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2011 at 5:36 | comment | added | Harry Gindi | Dear Emily, Joyal feels the same way. The term that he prefers is the "canonical" model structure. Here's a link to his explanation: math.ntnu.no/~stacey/Mathforge/nForum/… | |
| Feb 6, 2011 at 22:08 | comment | added | Emily Riehl | No, I meant the one with weak equivalences the categorical equivalences, fibrations the isofibrations, and cofibrations functors injective on objects. I often call this the ``folk'' model structure, but I seem to remember that Steve Lack, who has written on this sort of thing, doesn't like that name for some reason. | |
| Feb 6, 2011 at 20:55 | comment | added | Tyler Lawson | Thanks a lot for your comments. Is the "usual" model category structure on Cat that you describe the one due to Thomason? | |
| Feb 6, 2011 at 20:04 | comment | added | Emily Riehl | I should have said, you technically only need $R'$ to lift through the category of algebras for the pointed endofunctor part of the monad $\mathbb{R}$ (meaning, you can drop the coherence condition for the multiplication). This functor exists if and only if the arrows in the image of $R'$ lift naturally against their left factors with respect to the functorial factorization of $(\mathbb{L},\mathbb{R})$. And dually of course. | |
| Feb 6, 2011 at 19:34 | history | answered | Emily Riehl | CC BY-SA 2.5 |