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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeDec 17th 2014
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexSomeone (anonymous) has raised a query at [[quality type]]. They say: > (Is “consists entirely of idempotents” correct?)

   Someone (anonymous) has raised a query at quality type. They say:

   (Is “consists entirely of idempotents” correct?)

2. • CommentRowNumber2.
   • CommentAuthorThomas Holder
   • CommentTimeDec 17th 2014
   • (edited Dec 19th 2014)
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexWell, yes! $\Delta_1=\{1,\partial_0,\partial_1\}$ and $\partial_i\partial_i=\partial_i$ from setting $i=j$ in the multiplication table. In general, [[graphic monoids]] consist entirely of idempotents. Perhaps the entry's wording is suggesting that the Morita equivalent diagram category consists entirely of idempotents which is probably false!? [add.: Well, the diagram category has morphisms that are not even endomorphisms so 'probably false' reads 'obviously false'. By the way, Tim, thanks for catching the query!]

   Well, yes! $\Delta_1=\{1,\partial_0,\partial_1\}$ and $\partial_i\partial_i=\partial_i$ from setting $i=j$ in the multiplication table. In general, graphic monoids consist entirely of idempotents.

   Perhaps the entry’s wording is suggesting that the Morita equivalent diagram category consists entirely of idempotents which is probably false!?

   [add.: Well, the diagram category has morphisms that are not even endomorphisms so ’probably false’ reads ’obviously false’. By the way, Tim, thanks for catching the query!]