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1. • CommentRowNumber1.
   • CommentAuthorvarkor
   • CommentTimeDec 10th 2018
   • PermaLink
   Author: varkor
   Format: MarkdownItexFix duplicate redirect. <a href="https://ncatlab.org/nlab/revision/diff/terminal+coalgebra+for+an+endofunctor/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/terminal+coalgebra+for+an+endofunctor/28">v28</a>, <a href="https://ncatlab.org/nlab/show/terminal+coalgebra+for+an+endofunctor">current</a>

   Fix duplicate redirect.

   diff, v28, current

2. • CommentRowNumber2.
   • CommentAuthornLab edit announcer
   • CommentTimeNov 30th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexremoving duplicate redirects Anonymous <a href="https://ncatlab.org/nlab/revision/diff/terminal+coalgebra+for+an+endofunctor/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/terminal+coalgebra+for+an+endofunctor/30">v30</a>, <a href="https://ncatlab.org/nlab/show/terminal+coalgebra+for+an+endofunctor">current</a>

   removing duplicate redirects

   Anonymous

   diff, v30, current

3. • CommentRowNumber3.
   • CommentAuthornLab edit announcer
   • CommentTimeNov 30th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexadding some redirects "terminal coalgebra for an endofunctor", "terminal coalgebras for an endofunctor", "terminal coalgebra for the endofunctor", "terminal coalgebras for the endofunctor" Anonymous <a href="https://ncatlab.org/nlab/revision/diff/terminal+coalgebra+for+an+endofunctor/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/terminal+coalgebra+for+an+endofunctor/30">v30</a>, <a href="https://ncatlab.org/nlab/show/terminal+coalgebra+for+an+endofunctor">current</a>

   adding some redirects “terminal coalgebra for an endofunctor”, “terminal coalgebras for an endofunctor”, “terminal coalgebra for the endofunctor”, “terminal coalgebras for the endofunctor”

   Anonymous

   diff, v30, current

4. • CommentRowNumber4.
   • CommentAuthornLab edit announcer
   • CommentTimeNov 30th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexalso removing duplicate redirect for terminal coalgebra Anonymous <a href="https://ncatlab.org/nlab/revision/diff/terminal+coalgebra+for+an+endofunctor/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/terminal+coalgebra+for+an+endofunctor/30">v30</a>, <a href="https://ncatlab.org/nlab/show/terminal+coalgebra+for+an+endofunctor">current</a>

   also removing duplicate redirect for terminal coalgebra

   Anonymous

   diff, v30, current

5. • CommentRowNumber5.
   • CommentAuthorMatthias Hutzler
   • CommentTimeApr 4th 2023
   • (edited Apr 4th 2023)
   • PermaLink
   Author: Matthias Hutzler
   Format: MarkdownItexHi! The page claims that the terminal coalgebra is the largest fixed point in that the unique coalgebra map "is an injection if C is Set". Am I missing an implicit assumption here? If we take for example $F = Id_{Set}$, then the terminal coalgebra is $1 \to 1$, and most fixed points of $Id_{Set}$ don't embed into $1$. My current understanding is that the "largest fixed point" claim is only true if we take "largest" as an informal word for "terminal". But if there is more to it then I would like to understand it.

   Hi! The page claims that the terminal coalgebra is the largest fixed point in that the unique coalgebra map “is an injection if C is Set”. Am I missing an implicit assumption here? If we take for example $F = Id_{Set}$, then the terminal coalgebra is $1 \to 1$, and most fixed points of $Id_{Set}$ don’t embed into $1$.

   My current understanding is that the “largest fixed point” claim is only true if we take “largest” as an informal word for “terminal”. But if there is more to it then I would like to understand it.

6. • CommentRowNumber6.
   • CommentAuthorTodd_Trimble
   • CommentTimeApr 5th 2023
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexAgreed; this doesn't make sense as written. The mistake first appeared in Revision 2. Strange that nobody before now (including me) seems to have picked up on it. It's true that in many cases, the initial algebra for an endofunctor on $Set$ seems to embed in the terminal coalgebra (I don't know off-hand just how general that is, but one idea that works in many cases is to construct the initial algebra as a colimit of the well-founded subcoalgebras of the terminal coalgebra, along the lines of Paul Taylor's book). Possibly Toby was generalizing hastily from some such observation.

   Agreed; this doesn’t make sense as written. The mistake first appeared in Revision 2. Strange that nobody before now (including me) seems to have picked up on it.

   It’s true that in many cases, the initial algebra for an endofunctor on $Set$ seems to embed in the terminal coalgebra (I don’t know off-hand just how general that is, but one idea that works in many cases is to construct the initial algebra as a colimit of the well-founded subcoalgebras of the terminal coalgebra, along the lines of Paul Taylor’s book). Possibly Toby was generalizing hastily from some such observation.