<br style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;" class="gmail_quote"><blockquote>Here F is the identity functor, and G is the list functor. And yes, C=D=<br>
category of (a subset of) Haskell types.<br></blockquote><br>Are you saying the function that goes from list functor to singleton funtor is a natural transformation? <br><br>But aren't they functors to different subset of Haskell Types?<br>
<br>The Haskell Wikibooks also <a href="http://en.wikibooks.org/wiki/Haskell/Category_theory#Functors_on_Hask">says</a> the same thing: <br><blockquote style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;" class="gmail_quote">
Functors in Haskell are from <b>Hask</b> to <i>func</i>, where <i>func</i> is the subcategory of <b>Hask</b> defined on just that functor's types. E.g. the list functor goes from <b>Hask</b> to <b>Lst</b>, where <b>Lst</b> is the category containing only <i>list types</i>, that is, <code>[T]</code> for any type <code>T</code>. The morphisms in <b>Lst</b> are functions defined on list types, that is, functions <code>[T] -> [U]</code> for types <code>T</code>, <code>U</code>.<br>
<br></blockquote><br>So in your example there is C that is Hask. But there are two D's, D1 that is all List types, and D2 all singleton types. In this example I guess, the Singleton types are subset of List types which are subset of Hask. Is that related to natural transformation or unrelated?<br>
<br>Daryoush<br><br><br><div class="gmail_quote">On Wed, Apr 22, 2009 at 12:18 AM, Kim-Ee Yeoh <span dir="ltr"><<a href="mailto:a.biurvOir4@asuhan.com">a.biurvOir4@asuhan.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div class="im"><br>
<br>
Daryoush Mehrtash-2 wrote:<br>
><br>
> I am not sure I follow how the endofunctor gave me the 2nd functor.<br>
><br>
> As I read the transformation there are two catagories C and D and two<br>
> functors F and G between the same two catagories. My problem is that I<br>
> only<br>
> have one functor between the Hask and List catagories. So where does the<br>
> 2nd functor come into picture that also maps between the same C and D<br>
> catagories?<br>
><br>
<br>
</div>Consider<br>
singleton :: a -> [a]<br>
singleton x = [x]<br>
<br>
Here F is the identity functor, and G is the list functor. And yes, C=D=<br>
category of (a subset of) Haskell types.<br>
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</div></div></blockquote></div><br><br clear="all"><br>-- <br>Daryoush<br><br>Weblog: <a href="http://perlustration.blogspot.com/">http://perlustration.blogspot.com/</a><br>