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I have added some first content to generalized Reedy model structure.
I have been adding a bunch of further details to generalized Reedy model structure.
I wanted to break down the full proof into steps in a way that lends itself to presentation in a seminar. But I guess so far I mainly just copied it, just adding a few intermediate steps here and there. To be continued.
Okay, I have polished a bit more. Should now be readable and fairly complete.
Looking at Berger-Moerdijk’s article, it seems to me that a generalized Reedy category produces only model structures built out of the projective model structures on group actions; to use injective model structures one would need the dual notion (the definition of generalized Reedy category not being self-dual). This is what I get from their Remark 1.8. But our page generalized Reedy model structure seems to be saying that the same notion suffices for both kinds of model structure. Is that right?
Hm, I remember that issue from back when I wrote the entry (which was when I gave our group seminar about it). But I don’t remember now the argument. I’ll try to check.
There is a question about this article on MathOverflow: https://mathoverflow.net/questions/300326/reference-request-for-statement-on-nlab-reedy-cofibrancy-of-cosimplicial-ob
The claim discussed in the MathOverflow question was added by Urs Schreiber in revision 32.
Thanks for the alert! I forget what I thought when I wrote this in rev 32. For the moment I have implemented the most lazy fix now: this example.
Notice that this concerns the entry Reedy model structure, maybe we should move discussion to that thread
Urs, did you ever get anywhere with the issue discussed in #4-5 above? I would be a little surprised if one doesn’t have to switch to co-generalized Reedy categories when using injective model structures.
Sorry, no. It’s lost in time.
Okay, then I’ll edit our page to align with the published results.
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