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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeJan 18th 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThese look interesting for anyone interested in coinduction: * [http://www.cs.unibo.it/~sangio/IntroBook.html](http://www.cs.unibo.it/~sangio/IntroBook.html) * [http://www.cs.unibo.it/~sangio/AdvancedBook.html](http://www.cs.unibo.it/~sangio/AdvancedBook.html)

   These look interesting for anyone interested in coinduction:

   • http://www.cs.unibo.it/~sangio/IntroBook.html
   • http://www.cs.unibo.it/~sangio/AdvancedBook.html
2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 19th 2012
   • (edited Jan 19th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexnow also at _[Coinduction - References](http://ncatlab.org/nlab/show/coinduction#References)_. That entry would deserve to have something in its Examples-section.

   now also at Coinduction - References.

   That entry would deserve to have something in its Examples-section.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 19th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have also added * Bart Jacobs, Jan Rutten, _A tutorial on (Co)Algebras and (Co)Induction_ ([pdf](http://www.cs.ru.nl/~bart/PAPERS/JR.pdf))

   I have also added

   • Bart Jacobs, Jan Rutten, A tutorial on (Co)Algebras and (Co)Induction (pdf)
4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 19th 2012
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexWhy does it say at [[coinduction]]? >It generalises to corecursion. I thought corecursion concerns the existence of a morphism to the terminal coalgebra, and coinduction concerns the non-existenced of a proper quotient of the terminal coalgebra. We really need a proper discussion of bisimulation. Anyway, I pointed to an example of coinduction.

   Why does it say at coinduction?

   It generalises to corecursion.

   I thought corecursion concerns the existence of a morphism to the terminal coalgebra, and coinduction concerns the non-existenced of a proper quotient of the terminal coalgebra. We really need a proper discussion of bisimulation.

   Anyway, I pointed to an example of coinduction.

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 19th 2012
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThere's a handy discussion at Piponi's [blog](http://blog.sigfpe.com/2006/04/mongruences.html) as to why induction and coinduction seem so different. I guess it's because if they take place in a concrete category. one is using no proper subalgebra of the initial algebra, so no proper subset of a certain kind, while the other is using no proper quotient of the terminal algebra, so no equivalence relation of a certain kind.

   There’s a handy discussion at Piponi’s blog as to why induction and coinduction seem so different. I guess it’s because if they take place in a concrete category. one is using no proper subalgebra of the initial algebra, so no proper subset of a certain kind, while the other is using no proper quotient of the terminal algebra, so no equivalence relation of a certain kind.