Timeline for When do the Reedy and injective model category structures agree?
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| Mar 30, 2010 at 21:53 | comment | added | D.-C. Cisinski | The fact $\Theta_n$ has all the good properties follows from Lemma 2.4 in Clemens Berger's paper: "A cellular nerve for higher categories", Adv. Math. 169 (2002), no. 1, pp. 118-175. As an exercise, you may also prove directly that whenever $R$ is nice, so is its wreath product with $\Delta$ (in the sense of Definition 3.1 in this other paper of C. Berger: "Iterated wreath product of the simplex category and iterated loop spaces", Adv. Math. 213 (2007), no. 1, pp. 230-270); this would give another (and nicer) proof. | |
| Mar 30, 2010 at 21:28 | comment | added | Reid Barton | Thank you for the references. Do you have a convenient reference for the fact that $\Theta_n$ is a skeletal category? | |
| Mar 30, 2010 at 21:21 | comment | added | Charles Rezk | Cool. I'll take a look at it. I wish I'd known this was already in your paper; I've spent more time than I care to admit working this out. Can you say a word about why it works for $\Theta_n$? I think I have a proof, but maybe yours is better. | |
| Mar 30, 2010 at 21:04 | history | answered | D.-C. Cisinski | CC BY-SA 2.5 |