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1 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
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2 2009-03-27.txt:04:34:28: <oerjan> but functors and natural transformations are actually fairly _basic_ concepts in category theory
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3 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|
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4 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|
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5 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
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6 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.
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7 2011-03-04.txt:03:25:10: <MonadsSuck> too many functors and natural transformations
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8 2011-03-18.txt:19:32:07: <oerjan> there are natural transformations that make them almost inverses, though
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9 2011-03-18.txt:19:36:23: <oerjan> that it is a natural transformation, i presume
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10 2011-03-18.txt:19:36:55: <oklopol> oh one of those things natural transformations have between hom sets?
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11 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)
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12 2011-03-18.txt:19:38:55: <oklopol> a natural transformation between what functors?
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13 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"
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14 2011-03-18.txt:19:47:24: <copumpkin> we should legislate against unnatural transformations
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15 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
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16 2011-08-15.txt:22:42:02: <augur> natural transformations and adjunctions, for instance
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17 2011-08-15.txt:22:42:42: <augur> you need natural transformations before monads
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18 2011-08-15.txt:22:43:43: <augur> elliott_: haskell uses the relevant natural transformations you know
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19 2011-08-15.txt:22:44:40: <augur> but the natural transformation stuff perhaps!
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20 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.
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21 2011-08-15.txt:22:47:17: <augur> oerjan: parametric polymorphism is basically natural transformations
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22 2011-08-15.txt:22:47:51: <oklopol> surely it's natural transformations in some category
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23 2011-09-01.txt:01:16:40: <oerjan> there were some natural transformations and K-theory
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24 2011-10-01.txt:04:42:31: <CakeProphet> it's just that the eta for monads is a natural transformation.
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25 2011-10-02.txt:06:15:55: <oerjan> collect and uncollect are probably natural transformations
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26 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
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27 2011-10-02.txt:06:20:53: <oerjan> then collect . barrierFrontMap h = map h . collect, the equation for it being a natural transformation
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28 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.
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29 2012-01-27.txt:12:33:08: <oerjan> `run echo "A lens is a monoidal natural transformation between higher-order coalgebra functors" >wisdom/lens
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30 2012-01-27.txt:12:33:30: <HackEgo> A lens is a monoidal natural transformation between higher-order coalgebra functors
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31 2012-02-09.txt:22:17:08: <HackEgo> A lens is a monoidal natural transformation between higher-order coalgebra functors
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32 2012-03-01.txt:00:10:04: <tswett> What's up with natural transformations?
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33 2012-03-01.txt:00:10:18: <oerjan> `? natural transformation
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34 2012-03-01.txt:00:10:21: <HackEgo> natural transformation? ¯\(°_o)/¯
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35 2012-03-01.txt:00:11:00: <tswett> If that's what a functor is, is a natural transformation anything?
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36 2012-03-01.txt:00:11:19: <oerjan> `learn Natural transformations are just morphisms in the category of functors
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37 2012-03-01.txt:00:11:50: <oerjan> `run mv wisdom/natural wisdom/"natural transformation"
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38 2012-03-01.txt:00:12:00: <oerjan> `? natural transformation
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39 2012-03-01.txt:00:12:03: <HackEgo> Natural transformations are just morphisms in the category of functors
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40 2012-03-01.txt:00:13:12: <oerjan> tswett: the functors are the domains and codomains of the natural transformations.
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41 2012-03-01.txt:00:14:21: <itidus21> `pastelogs natural transformation
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