Comments on: On the Failure of Fixed-point Theorems for Chain-complete Lattices in the Effective Topos http://math.andrej.com/2009/01/23/on-the-failure-of-fixed-point-theorems-for-chain-complete-lattices-in-the-effective-topos/ Mathematics for computers Mon, 30 Jan 2012 07:14:48 +0000 hourly 1 http://wordpress.org/?v=3.2-beta2-18055 By: Andrej Bauer http://math.andrej.com/2009/01/23/on-the-failure-of-fixed-point-theorems-for-chain-complete-lattices-in-the-effective-topos/comment-page-1/#comment-11253 Andrej Bauer Mon, 26 Jan 2009 15:02:07 +0000 http://math.andrej.com/?p=159#comment-11253 Thank you for spotting that one. It should say that the diagonal map is an isomorphism, or equivalently epimorphism, as you suggest. Thank you for spotting that one. It should say that the diagonal map is an isomorphism, or equivalently epimorphism, as you suggest.

]]> By: p.l.lumsdaine http://math.andrej.com/2009/01/23/on-the-failure-of-fixed-point-theorems-for-chain-complete-lattices-in-the-effective-topos/comment-page-1/#comment-11236 p.l.lumsdaine Sat, 24 Jan 2009 03:26:30 +0000 http://math.andrej.com/?p=159#comment-11236 Very nice paper! I think there may be a typo in the first paragraph of Sect. 2, by the way: you define that X is discrete if the diagonal map X --> X^{\nabla 2} is _constant_. But if internally this is the condition that every map fron \nabla 2 to X is constant, i.e. in the image of the diagonal map, should the original condition be that the diagonal map is _epimorphic_? Very nice paper!

I think there may be a typo in the first paragraph of Sect. 2, by the way: you define that X is discrete if the diagonal map X –> X^{\nabla 2} is _constant_. But if internally this is the condition that every map fron \nabla 2 to X is constant, i.e. in the image of the diagonal map, should the original condition be that the diagonal map is _epimorphic_?

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