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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 28th 2013
   • (edited Jul 28th 2013)
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   Author: Urs
   Format: MarkdownItexadded a brief remark to _[[discrete object]]_ in a new section _[Examples --- in infintiy-toposes](http://ncatlab.org/nlab/show/discrete+object#ExamplesInInfinityToposes)_ on the relation between discreteness and cohomology. This is a (fairly trivial) comment on Mike's discussion over on the HoTT blog, linked to from the above.

   added a brief remark to discrete object in a new section Examples — in infintiy-toposes on the relation between discreteness and cohomology.

   This is a (fairly trivial) comment on Mike’s discussion over on the HoTT blog, linked to from the above.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeJul 28th 2013
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   Author: Todd_Trimble
   Format: MarkdownItexIn [[discrete object]] I spotted this statement > In [[Abstract Stone Duality]], a space is called __discrete__ if $X \times X \to X$ is open which didn't make a whole lot of sense to me; I figure what was really meant is that the diagonal $\delta: X \to X \times X$ is open, so I put that in instead. (Actually, it seems to me one wants to say that both $\delta$ and $\epsilon: X \to 1$ are open, but I don't have ASD in front of me and I'm not sure what Taylor does.)

   In discrete object I spotted this statement

   In Abstract Stone Duality, a space is called discrete if $X \times X \to X$ is open

   which didn’t make a whole lot of sense to me; I figure what was really meant is that the diagonal $\delta: X \to X \times X$ is open, so I put that in instead. (Actually, it seems to me one wants to say that both $\delta$ and $\epsilon: X \to 1$ are open, but I don’t have ASD in front of me and I’m not sure what Taylor does.)