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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJul 2nd 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexRemoved the following discussion: Discussion on a previous version of this entry: [[Mike Shulman|Mike]]: This term is kind of unfortunate; *simplicial weak $\omega$-category* could also mean a simplicial object in weak $\omega$-categories. I don't suppose we can do anything about that? [[Urs Schreiber|Urs]]: my impression is that what Dominic Verity mainly wants to express with the term is "simplicial model for weak $\omega$-category". Maybe we could/should use a longer phrase like that? [[Mike Shulman|Mike]]: That would make me happier. [[Urs Schreiber|Urs]]: okay, I changed it. Let me know if this is good now. _Toby_: But what about 'globular $\omega$-category' and things like that? Doesn\'t 'simplicial $\omega$-category' fit right into that framework? This page title sounds like an entire framework for defining $\omega$-category rather than a single $\omega$-category simplicially defined. [[Urs Schreiber|Urs]]: i am open to suggestions -- but notice that it does indeed seem to me that Dominic Verity wants to express "an entire framework for defining $\omega$-category", namely the framework where one skips over the attempt to define $\omega$-categories and instead tries to find a characterization of what should be their nerves. _Toby_: OK, that fits in with most of what\'s written here, but not the beginning >**Simplicial models for weak $\omega$-categories** -- sometimes called [[simplicial weak omega-category|simplicial weak ∞-categories]] -- are [...] Maybe that was just poorly written, but it threw me off. Should it be >A **simplicial model for weak $\omega$-categories** -- which are then sometimes called [[simplicial weak ∞-categories]] -- is [...] or even >A **simplicial model for weak $\omega$-categories** is [...] and only later mention [[simplicial weak ∞-categories]]? [[Mike Shulman|Mike]]: You're right that 'simplicial $\omega$-category' it fits into 'globular $\omega$-category' and 'opetopic $\omega$-category' and so on. It seems more problematic in this case, though, since simplicial objects of random categories are a good deal more prevalent than globular ones and opetopic ones. But perhaps I should just live with it. [[Urs Schreiber|Urs]]: I have now expanded the entry text on this point, trying to make very clear to the reader what's going on here. _Toby_: Thanks, that\'s much clearer. And if Verity\'s definition is at [[weak complicial set]], then we may not really need anything at [[simplicial weak ∞-category]], so no need to offend Mike\'s sensibilities (^_^) either. <a href="https://ncatlab.org/nlab/revision/diff/simplicial+model+for+weak+omega-categories/17">diff</a>, <a href="https://ncatlab.org/nlab/revision/simplicial+model+for+weak+omega-categories/17">v17</a>, <a href="https://ncatlab.org/nlab/show/simplicial+model+for+weak+omega-categories">current</a>

   Removed the following discussion:

   Discussion on a previous version of this entry:

   Mike: This term is kind of unfortunate; simplicial weak $\omega$-category could also mean a simplicial object in weak $\omega$-categories. I don’t suppose we can do anything about that?

   Urs: my impression is that what Dominic Verity mainly wants to express with the term is “simplicial model for weak $\omega$-category”. Maybe we could/should use a longer phrase like that?

   Mike: That would make me happier.

   Urs: okay, I changed it. Let me know if this is good now.

   Toby: But what about ’globular $\omega$-category’ and things like that? Doesn't ’simplicial $\omega$-category’ fit right into that framework? This page title sounds like an entire framework for defining $\omega$-category rather than a single $\omega$-category simplicially defined.

   Urs: i am open to suggestions – but notice that it does indeed seem to me that Dominic Verity wants to express “an entire framework for defining $\omega$-category”, namely the framework where one skips over the attempt to define $\omega$-categories and instead tries to find a characterization of what should be their nerves.

   Toby: OK, that fits in with most of what's written here, but not the beginning

   Simplicial models for weak $\omega$-categories – sometimes called simplicial weak ∞-categories – are […] Maybe that was just poorly written, but it threw me off. Should it be A simplicial model for weak $\omega$-categories – which are then sometimes called simplicial weak ∞-categories – is […] or even A simplicial model for weak $\omega$-categories is […] and only later mention simplicial weak ∞-categories?

   Mike: You’re right that ’simplicial $\omega$-category’ it fits into ’globular $\omega$-category’ and ’opetopic $\omega$-category’ and so on. It seems more problematic in this case, though, since simplicial objects of random categories are a good deal more prevalent than globular ones and opetopic ones. But perhaps I should just live with it.

   Urs: I have now expanded the entry text on this point, trying to make very clear to the reader what’s going on here.

   Toby: Thanks, that's much clearer. And if Verity's definition is at weak complicial set, then we may not really need anything at simplicial weak ∞-category, so no need to offend Mike's sensibilities (^_^) either.

   diff, v17, current