Timeline for Homotopy limit of model categories in the category of categories
Current License: CC BY-SA 4.0
8 events
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| Jun 25, 2018 at 1:13 | vote | accept | Dmitry Vaintrob | ||
| Jun 21, 2018 at 2:31 | comment | added | Dmitri Pavlov | @DavidWhite: She says there: “In practice, when the conditions of this theorem cannot be verified, we can still use the original levelwise model structure on L_D X and simply restrict to the appropriate subcategory when we want to require u and v to be weak equivalences.” I fail to see how such a claim could possibly solve the problem of constructing the pullback as a model category. | |
| Jun 21, 2018 at 2:26 | comment | added | Dmitri Pavlov | @DmitryVaintrob: u and v are forced to be weak equivalences once we pass to cofibrant objects. | |
| Jun 21, 2018 at 0:57 | comment | added | David White | @DmitriPavlov: She gives the indications about existence directly after finishing the proof of Theorem 3.2. Her first sentence there is "Of course, the di±culty in using this theorem lies in the difficulty in establishing that the model category $L_DX$ is right proper." | |
| Jun 21, 2018 at 0:56 | history | edited | David White | CC BY-SA 4.0 |
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| Jun 20, 2018 at 19:05 | comment | added | Dmitry Vaintrob | This is a little surprising: it sounds like you're describing the Grothendieck construction, which is some kind of (infinity, 2)-categorical pullback, and not the (infinity, 1) categorical pullback. Are you sure your u, v are not required to be weak equivalences of some kind? | |
| Jun 20, 2018 at 17:40 | comment | added | Dmitri Pavlov | Where exactly in her paper does Julie Bergner prove that “This category M can be given a model structure where the weak equivalences and cofibrations are levelwise (on each x_i)”? In Theorem 3.2 she assumes that “L_D X has the structure of a right proper model category” without giving any indications as to its existence. | |
| Jun 20, 2018 at 2:04 | history | answered | David White | CC BY-SA 4.0 |