Timeline for A categorical characterization of ordinal numbers

8 events

when toggle format	what		by	license	comment
May 22, 2014 at 17:39	vote	accept	fosco
May 21, 2014 at 11:10	comment	added	Giorgio Mossa		I guess that for help could be useful to characterize $\star$ by universal property, otherwise is not clear what a category (not necessarily a subcategory of $\mathbf{Cat}$) closed by $\star$ should be.
May 21, 2014 at 8:18	answer	added	Paul Taylor		timeline score: 6
May 20, 2014 at 14:36	comment	added	Giorgio Mossa		Note that in the note you have linked Joyal define $\star B$ as a functor of type $\mathbf {Cat} \to B\setminus \mathbf {Cat}$ not $\mathbf {Cat} \to \mathbf {Cat}$.
May 20, 2014 at 14:34	comment	added	Giorgio Mossa		The operation $\star$ does not commute with colimit: indeed if that where true then for every limit ordinal $\lambda=\bigcup_{\gamma < \lambda} \gamma$ you should have that $\lambda+1=\lambda\star[0]=\bigcup_{\gamma < \lambda} \gamma\star[0]=\bigcup_{\gamma < \lambda}\gamma+1=\lambda$ things that's not possible since $\lambda$ doesn't have a max while $\lambda+1$ does.
May 20, 2014 at 14:16	history	edited	fosco	CC BY-SA 3.0	added 211 characters in body
May 20, 2014 at 14:01	history	edited	fosco	CC BY-SA 3.0	added 19 characters in body
May 20, 2014 at 13:45	history	asked	fosco	CC BY-SA 3.0