annotate paste/paste.7952 @ 9285:8320c9c4620f

<oerjan> learn Umlaut is German for "hum aloud", an important feature of the German language. It is indicated by putting two dots over the vowel of the syllable.
author HackBot
date Sat, 15 Oct 2016 00:04:47 +0000
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49ec0dc3a516 <itidus21> pastelogs natural transformation
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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
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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|
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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|
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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.
49ec0dc3a516 <itidus21> pastelogs natural transformation
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7 2011-03-04.txt:03:25:10: <MonadsSuck> too many functors and natural transformations
49ec0dc3a516 <itidus21> pastelogs natural transformation
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8 2011-03-18.txt:19:32:07: <oerjan> there are natural transformations that make them almost inverses, though
49ec0dc3a516 <itidus21> pastelogs natural transformation
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9 2011-03-18.txt:19:36:23: <oerjan> that it is a natural transformation, i presume
49ec0dc3a516 <itidus21> pastelogs natural transformation
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10 2011-03-18.txt:19:36:55: <oklopol> oh one of those things natural transformations have between hom sets?
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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)
49ec0dc3a516 <itidus21> pastelogs natural transformation
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12 2011-03-18.txt:19:38:55: <oklopol> a natural transformation between what functors?
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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"
49ec0dc3a516 <itidus21> pastelogs natural transformation
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14 2011-03-18.txt:19:47:24: <copumpkin> we should legislate against unnatural transformations
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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
49ec0dc3a516 <itidus21> pastelogs natural transformation
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16 2011-08-15.txt:22:42:02: <augur> natural transformations and adjunctions, for instance
49ec0dc3a516 <itidus21> pastelogs natural transformation
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17 2011-08-15.txt:22:42:42: <augur> you need natural transformations before monads
49ec0dc3a516 <itidus21> pastelogs natural transformation
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18 2011-08-15.txt:22:43:43: <augur> elliott_: haskell uses the relevant natural transformations you know
49ec0dc3a516 <itidus21> pastelogs natural transformation
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19 2011-08-15.txt:22:44:40: <augur> but the natural transformation stuff perhaps!
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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.
49ec0dc3a516 <itidus21> pastelogs natural transformation
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21 2011-08-15.txt:22:47:17: <augur> oerjan: parametric polymorphism is basically natural transformations
49ec0dc3a516 <itidus21> pastelogs natural transformation
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22 2011-08-15.txt:22:47:51: <oklopol> surely it's natural transformations in some category
49ec0dc3a516 <itidus21> pastelogs natural transformation
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23 2011-09-01.txt:01:16:40: <oerjan> there were some natural transformations and K-theory
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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.
49ec0dc3a516 <itidus21> pastelogs natural transformation
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25 2011-10-02.txt:06:15:55: <oerjan> collect and uncollect are probably natural transformations
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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
49ec0dc3a516 <itidus21> pastelogs 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.
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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
49ec0dc3a516 <itidus21> pastelogs natural transformation
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32 2012-03-01.txt:00:10:04: <tswett> What's up with natural transformations?
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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)/¯
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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?
49ec0dc3a516 <itidus21> pastelogs natural transformation
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36 2012-03-01.txt:00:11:19: <oerjan> `learn Natural transformations are just morphisms in the category of functors
49ec0dc3a516 <itidus21> pastelogs natural transformation
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37 2012-03-01.txt:00:11:50: <oerjan> `run mv wisdom/natural wisdom/"natural transformation"
49ec0dc3a516 <itidus21> pastelogs 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
49ec0dc3a516 <itidus21> pastelogs natural transformation
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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.
49ec0dc3a516 <itidus21> pastelogs natural transformation
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41 2012-03-01.txt:00:14:21: <itidus21> `pastelogs natural transformation