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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeAug 30th 2015
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   Author: Todd_Trimble
   Format: MarkdownItexI have been adding some material to [[Cocomm Coalg]]. I'm not sure where I first read that this category is extensive, and hope that a relatively painless proof of that can be produced.

   I have been adding some material to Cocomm Coalg. I’m not sure where I first read that this category is extensive, and hope that a relatively painless proof of that can be produced.

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeAug 31st 2015
   • (edited Aug 31st 2015)
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   Author: DavidRoberts
   Format: MarkdownItexIt looks like [this article](http://dx.doi.org/10.1016/S0304-3975(02)00582-0) is enough to get distributivity for certain categories of coalgebras for endofunctors on $Set$. In fact that paper shows (Proposition 3) that for an preimage-preserving endofunctor $F$ on an extensive category $C$, the category of coalgebras is also extensive. Infinitary extensivity works analogously. [On the structure of categories of coalgebras](http://dx.doi.org/10.1016/S0304-3975(00)00124-9) might also be useful.

   It looks like this article is enough to get distributivity for certain categories of coalgebras for endofunctors on $Set$.

   In fact that paper shows (Proposition 3) that for an preimage-preserving endofunctor $F$ on an extensive category $C$, the category of coalgebras is also extensive. Infinitary extensivity works analogously.

   On the structure of categories of coalgebras might also be useful.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeAug 31st 2015
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   Author: Todd_Trimble
   Format: MarkdownItexI had seen that first article you mentioned. I can't see that gives directly what I'm after, since extensivity of $Set$ is needed and the category of modules on which there is a comonad whose coalgebra category is [[Cocomm Coalg]] is not extensive. But it does have some nice material, some of which I've been meaning to add to [[taut functor]]. Actually, both articles look interesting -- thanks!

   I had seen that first article you mentioned. I can’t see that gives directly what I’m after, since extensivity of $Set$ is needed and the category of modules on which there is a comonad whose coalgebra category is Cocomm Coalg is not extensive. But it does have some nice material, some of which I’ve been meaning to add to taut functor.

   Actually, both articles look interesting – thanks!

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeAug 31st 2015
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   Author: DavidRoberts
   Format: MarkdownItexAh, I see: I'm not familiar with coalgebras, as no doubt you could tell.

   Ah, I see: I’m not familiar with coalgebras, as no doubt you could tell.