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    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeDec 10th 2018

    Fix duplicate redirect.

    diff, v28, current

  1. removing duplicate redirects

    Anonymous

    diff, v30, current

  2. 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

  3. also removing duplicate redirect for terminal coalgebra

    Anonymous

    diff, v30, current

    • CommentRowNumber5.
    • CommentAuthorMatthias Hutzler
    • CommentTimeApr 4th 2023
    • (edited Apr 4th 2023)

    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 SetF = Id_{Set}, then the terminal coalgebra is 111 \to 1, and most fixed points of Id SetId_{Set} don’t embed into 11.

    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.

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 5th 2023

    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 SetSet 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.