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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 2nd 2009
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownDoes anyone reading this know some nice conditions under which, given an endofunctor <latex>F: C \to C</latex> on a cartesian closed category for which the end <latex>\int_{c: C} c^{c^{F c}}</latex> exists, that this is the initial algebra for <latex>F</latex>? I can prove without any more extra assumptions that this end carries a weakly initial <latex>F</latex>-algebra structure, but I can't prove it to be initial in general. I thought I recalled seeing discussion about this somewhere, but I don't recall where.

   Does anyone reading this know some nice conditions under which, given an endofunctor on a cartesian closed category for which the end

   

   exists, that this is the initial algebra for ? I can prove without any more extra assumptions that this end carries a weakly initial -algebra structure, but I can't prove it to be initial in general. I thought I recalled seeing discussion about this somewhere, but I don't recall where.

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeDec 4th 2009
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   Author: TobyBartels
   Format: MarkdownI don't know either, but I'd like to see the answer. Have you tried the [categories mailing list](http://www.mta.ca/~cat-dist/) or [MathOverlow](http://mathoverflow.net/)?

   I don't know either, but I'd like to see the answer. Have you tried the categories mailing list or MathOverlow?