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1. • CommentRowNumber1.
   • CommentAuthorGuest
   • CommentTimeMay 21st 2023
   • PermaLink
   Author: Guest
   Format: MarkdownItexstarting page on concrete (infinity,1)-categories <a href="https://ncatlab.org/nlab/revision/concrete+%28infinity%2C1%29-category/1">v1</a>, <a href="https://ncatlab.org/nlab/show/concrete+%28infinity%2C1%29-category">current</a>

   starting page on concrete (infinity,1)-categories

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 21st 2023
   • (edited May 21st 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe entry currently says: > We say an (infinity,1)-category C is concretizable if and only if it admits a (infinity,1)-functor $U \colon C \to \infty Grpd$. This is an empty request. Every $\infty$-category admits such a functor. Take for instance any constant $\infty$-functor $C \to \ast \to \infty Grpd$. If you really don't want to impose any condition on the $\infty$-functor to $\infty Grpd$, then you should speak of the specification of such a functor not as a *property* but as *[[extra structure]]*.

   The entry currently says:

   We say an (infinity,1)-category C is concretizable if and only if it admits a (infinity,1)-functor $U \colon C \to \infty Grpd$.

   This is an empty request. Every $\infty$-category admits such a functor. Take for instance any constant $\infty$-functor $C \to \ast \to \infty Grpd$.

   If you really don’t want to impose any condition on the $\infty$-functor to $\infty Grpd$, then you should speak of the specification of such a functor not as a property but as extra structure.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 21st 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexFor instance, you might want to say that "concrete $\infty$-categories" are the objects of the *slice* $(\infty,1)Cat_{/\infty Grpd}$. Of course, whether this is the right definition depends on what one wants to do with it. Where are you headed with this?

   For instance, you might want to say that “concrete $\infty$-categories” are the objects of the slice $(\infty,1)Cat_{/\infty Grpd}$.

   Of course, whether this is the right definition depends on what one wants to do with it. Where are you headed with this?