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Mon, 14 Jul 2014 20:44:36 +0000hourly1http://wordpress.com/Comment on Abstraction, intuition, and the “monad tutorial fallacy” by Abstractor
http://byorgey.wordpress.com/2009/01/12/abstraction-intuition-and-the-monad-tutorial-fallacy/#comment-13249
Mon, 14 Jul 2014 20:44:36 +0000http://byorgey.wordpress.com/?p=108#comment-13249Very insightful article which went from teaching the “monad tutorial fallacy” to the more abstract “tutorial fallacy”. Thank you.
]]>Comment on AC and equivalence of categories by Brent
http://byorgey.wordpress.com/2014/06/05/ac-and-equivalence-of-categories/#comment-13207
Fri, 20 Jun 2014 10:40:33 +0000http://byorgey.wordpress.com/?p=1264#comment-13207Oh, haha, three, not tree. Yes, there are two Rose trees with three leaves, not one. Anyway, good, I’m glad you figured it out. And indeed, this is a staple combinatorics brainteaser/exercise, I think it is also in Bergeron et al. and it’s also in my species paper from the 2010 Haskell Symposium.
]]>Comment on AC and equivalence of categories by sclvsclv
http://byorgey.wordpress.com/2014/06/05/ac-and-equivalence-of-categories/#comment-13206
Fri, 20 Jun 2014 02:57:33 +0000http://byorgey.wordpress.com/?p=1264#comment-13206Ah pardon me. “three-leaved tree”. Looking at the types I see my exact notion was off because I misread them . The above comment was me just being flummoxed by your non-obvious exercise. I now have figured out your exercise, then went and checked and found that Hinze and James explained it in “Reason Isomorphically!” Thanks for a good brain teaser.
]]>Comment on AC and equivalence of categories by Brent
http://byorgey.wordpress.com/2014/06/05/ac-and-equivalence-of-categories/#comment-13204
Fri, 20 Jun 2014 01:01:34 +0000http://byorgey.wordpress.com/?p=1264#comment-13204No, they are definitely equivalent. I have the Agda code here to prove it. I agree that List and Fork are not equivalent; they don’t even have the same number of structures of size zero (List: 1, Fork: 0). I don’t quite understand your comment about encoding a “tree-leaved tree” (what is that?), but I think perhaps you are confused about what it means for Fork and Rose to be equivalent.
]]>Comment on AC and equivalence of categories by sclv
http://byorgey.wordpress.com/2014/06/05/ac-and-equivalence-of-categories/#comment-13202
Thu, 19 Jun 2014 23:09:19 +0000http://byorgey.wordpress.com/?p=1264#comment-13202I’m fairly certain that Fork and Rose are not equivalent, although they are adjoint. There are “two ways” for example to encode a tree-leaved tree with Fork, but there is only one way with Rose. This is the same reason, in essence, that List and Fork are not equivalent, but are adjoint (after all one degenerate form of Rose [depth 1 trees] is isomorphic to the class of all lists).
]]>Comment on AC and equivalence of categories by Anafunctors | blog :: Brent -> [String]
http://byorgey.wordpress.com/2014/06/05/ac-and-equivalence-of-categories/#comment-13194
Mon, 16 Jun 2014 20:10:57 +0000http://byorgey.wordpress.com/?p=1264#comment-13194[…] ← AC and equivalence of categories […]
]]>Comment on Unique isomorphism and generalized “the” by Anafunctors | blog :: Brent -> [String]
http://byorgey.wordpress.com/2014/05/13/unique-isomorphism-and-generalized-the/#comment-13193
Mon, 16 Jun 2014 20:10:55 +0000http://byorgey.wordpress.com/?p=1250#comment-13193[…] is part four in a series of posts on avoiding the axiom of choice (part one, part two, part […]
]]>Comment on Avoiding the axiom of choice, part I by Anafunctors | blog :: Brent -> [String]
http://byorgey.wordpress.com/2014/05/08/avoiding-the-axiom-of-choice-part-i/#comment-13192
Mon, 16 Jun 2014 20:10:53 +0000http://byorgey.wordpress.com/?p=1226#comment-13192[…] is part four in a series of posts on avoiding the axiom of choice (part one, part two, part […]
]]>Comment on Unique isomorphism and generalized “the” by AC and equivalence of categories | blog :: Brent -> [String]
http://byorgey.wordpress.com/2014/05/13/unique-isomorphism-and-generalized-the/#comment-13185
Tue, 10 Jun 2014 21:16:08 +0000http://byorgey.wordpress.com/?p=1250#comment-13185[…] ← Unique isomorphism and generalized “the” […]
]]>Comment on Avoiding the axiom of choice, part I by AC and equivalence of categories | blog :: Brent -> [String]
http://byorgey.wordpress.com/2014/05/08/avoiding-the-axiom-of-choice-part-i/#comment-13184
Tue, 10 Jun 2014 21:16:05 +0000http://byorgey.wordpress.com/?p=1226#comment-13184[…] is part three in a series of posts on avoiding the axiom of choice (part one, part […]
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