Timeline for Model category of diagrams with the colimit detecting the weak equivalences
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2018 at 12:53 | answer | added | Ben | timeline score: 4 | |
| Jul 23, 2018 at 7:58 | comment | added | Philippe Gaucher | @SimonHenry okay I understand the mistake in my intuition now. | |
| Jul 20, 2018 at 14:58 | comment | added | Mike Shulman | Right - what "left induced" means is that, as I said, we define a map of diagrams to be a cofibration or a weak equivalence if its colimit is such. This means such a model structure would not be the projective one, and would be an answer to your question, if it exists. But you'd have to look at the conditions for such a model structure to exist and check whether they hold. | |
| Jul 20, 2018 at 14:46 | comment | added | Simon Henry | It takes fibrations and trivial fibrations to very specific objectwise fibrations and trivial fibrations that are from generating the whole projective model structure. So It is not sufficient to deduce that it is the projective model structure. If the structure that Mike mention exists then it answer your questions, but I guess it is not going to exists in general. | |
| Jul 20, 2018 at 8:43 | comment | added | Philippe Gaucher | @MikeShulman Naively I believed that the transport of model structures would give the projective model structure since the right adjoint (the constant diagram functors) takes (trivial) fibrations to objectwise (trivial) fibrations. And a model structure is determined by these two classes of maps. | |
| Jul 20, 2018 at 8:21 | comment | added | Mike Shulman | One thing to try would be to "left induce" a model structure along the colimit functor since it is a left adjoint: define the cofibrations as well as the weak equivalences to be created by colimits. There are some links to papers about left induced model structures at the bottom of ncatlab.org/nlab/show/transferred+model+structure. | |
| Jul 20, 2018 at 7:37 | history | asked | Philippe Gaucher | CC BY-SA 4.0 |