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<oerjan> le/rn soviet union/In ancient history, the Soviet Union used to be the THEM. They believed in absurd principles like "Better Red than Dead". Then Ronald Reagan invented Star Wars to destroy it, after which there seemed to be no the THEM for a while.
author | HackBot |
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date | Tue, 16 Feb 2016 21:39:22 +0000 |
parents | 49ec0dc3a516 |
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2009-03-27.txt:04:31:30: <oerjan> and then you define a category where the objects are _functors_, and the morphisms are something called natural transformations 2009-03-27.txt:04:34:28: <oerjan> but functors and natural transformations are actually fairly _basic_ concepts in category theory 2009-03-27.txt:04:35:54: <oklowob> <oerjan> but functors and natural transformations are actually fairly _basic_ concepts in category theory <<< yeah okay i'm getting a boner here where can i learn this stuff 8| 2009-03-27.txt:15:48:21: <ehird> 03:35 oklowob: <oerjan> but functors and natural transformations are actually fairly _basic_ concepts in category theory <<< yeah okay i'm getting a boner here where can i learn this stuff 8| 2010-12-27.txt:01:24:47: <j-invariant> btw, if eta : F --> G is a natural transformation for functors F,G : C --> D. Then X : C |- etaX : FX --> GX 2011-02-02.txt:21:01:06: <elliott> Used when you really need both semi-mutual recursion and history and to repeatedly apply a natural transformation as you get deeper into the functor. Zygo implements semi-mutual recursion like a zygomorphism. Para gives you access to your result à la paramorphism. 2011-03-04.txt:03:25:10: <MonadsSuck> too many functors and natural transformations 2011-03-18.txt:19:32:07: <oerjan> there are natural transformations that make them almost inverses, though 2011-03-18.txt:19:36:23: <oerjan> that it is a natural transformation, i presume 2011-03-18.txt:19:36:55: <oklopol> oh one of those things natural transformations have between hom sets? 2011-03-18.txt:19:38:21: <oerjan> the bijection should _be_ a natural transformation when restricted to each variable (and taking the most obvious functors to be a transformation between) 2011-03-18.txt:19:38:55: <oklopol> a natural transformation between what functors? 2011-03-18.txt:19:42:21: <oerjan> and the bijection being a natural transformation between those is what it means to be "natural in Y" 2011-03-18.txt:19:47:24: <copumpkin> we should legislate against unnatural transformations 2011-03-18.txt:20:30:26: <oklopol> i'm sure this would be perfectly easy on paper, but i still find natural transformations kinda hard to picture when they occur in a "concrete" situation 2011-08-15.txt:22:42:02: <augur> natural transformations and adjunctions, for instance 2011-08-15.txt:22:42:42: <augur> you need natural transformations before monads 2011-08-15.txt:22:43:43: <augur> elliott_: haskell uses the relevant natural transformations you know 2011-08-15.txt:22:44:40: <augur> but the natural transformation stuff perhaps! 2011-08-15.txt:22:46:48: <oerjan> <elliott_> augur: So it'll be trying to cover only that CT that Haskell uses <-- but you need natural transformations to properly understand parametricity. i think. 2011-08-15.txt:22:47:17: <augur> oerjan: parametric polymorphism is basically natural transformations 2011-08-15.txt:22:47:51: <oklopol> surely it's natural transformations in some category 2011-09-01.txt:01:16:40: <oerjan> there were some natural transformations and K-theory 2011-10-01.txt:04:42:31: <CakeProphet> it's just that the eta for monads is a natural transformation. 2011-10-02.txt:06:15:55: <oerjan> collect and uncollect are probably natural transformations 2011-10-02.txt:06:17:38: <oerjan> collect is a natural transformation from the functor Barrier _ () t to the functor [_], although only the second one is a Functor in the haskell sense 2011-10-02.txt:06:20:53: <oerjan> then collect . barrierFrontMap h = map h . collect, the equation for it being a natural transformation 2012-01-08.txt:18:06:21: <Phantom_Hoover> Like, he defines and explains natural transformations in half a page, and then gives examples for the next two. 2012-01-27.txt:12:33:08: <oerjan> `run echo "A lens is a monoidal natural transformation between higher-order coalgebra functors" >wisdom/lens 2012-01-27.txt:12:33:30: <HackEgo> A lens is a monoidal natural transformation between higher-order coalgebra functors 2012-02-09.txt:22:17:08: <HackEgo> A lens is a monoidal natural transformation between higher-order coalgebra functors 2012-03-01.txt:00:10:04: <tswett> What's up with natural transformations? 2012-03-01.txt:00:10:18: <oerjan> `? natural transformation 2012-03-01.txt:00:10:21: <HackEgo> natural transformation? ¯\(°_o)/¯ 2012-03-01.txt:00:11:00: <tswett> If that's what a functor is, is a natural transformation anything? 2012-03-01.txt:00:11:19: <oerjan> `learn Natural transformations are just morphisms in the category of functors 2012-03-01.txt:00:11:50: <oerjan> `run mv wisdom/natural wisdom/"natural transformation" 2012-03-01.txt:00:12:00: <oerjan> `? natural transformation 2012-03-01.txt:00:12:03: <HackEgo> Natural transformations are just morphisms in the category of functors 2012-03-01.txt:00:13:12: <oerjan> tswett: the functors are the domains and codomains of the natural transformations. 2012-03-01.txt:00:14:21: <itidus21> `pastelogs natural transformation