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expanded (infinity,1)-category of (infinity,1)-functors : more details, more statements, more proofs. In particular concerning the model by the global model structure on functors.
added remakrs and pointers from global model structure on functors to (infinity,1)-category of (infinity,1)-functors.
What I still don't fully know is the general statement what invariant notion precisely the Reedy model structures model.
Since the weak equivalences in the Reedy model structure are the same as those in the projective and injective model structures, it should model the same -category, no?
Right. But the Reedy model structure exists without assumptions on the codomain. What if the codomain is not combinatorial, for instance? Does the Reedy model structure still present the (oo,1)-functor (oo,1)-category?
In any case, I see that some polishing of the discussion of the relation to the proj/in j-structure at Reedy model structure was in order: created section Properties.
Good question. I would be surprised if the answer were no, but I don't actually know. Note that the projective model structure requires the codomain only to be cofibrantly generated. There do, of course, exist model categories that aren't cofibrantly generated.
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