<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">I’d recommend *not* reading Categories for the Working Mathematician unless you are a mathematician (lots of background assumed) and even then it’s a bit of a dull read.</div><div class=""><br class=""></div><div class="">
<div style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;">Dominic Steinitz<br class=""><a href="mailto:dominic@steinitz.org" class="">dominic@steinitz.org</a><br class="">http://idontgetoutmuch.org<br class="">Twitter: @idontgetoutmuch</div>
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<br class=""><div><blockquote type="cite" class=""><div class=""><div class="">From: Viktor Dukhovni <<a href="mailto:ietf-dane@dukhovni.org" class="">ietf-dane@dukhovni.org</a>><br class="">To: <a href="mailto:haskell-cafe@haskell.org" class="">haskell-cafe@haskell.org</a><br class="">Subject: Re: [Haskell-cafe] Haskell function composition commutivity?<br class="">Message-ID: <<a href="mailto:YHYPMnJcYzdEolzl@straasha.imrryr.org" class="">YHYPMnJcYzdEolzl@straasha.imrryr.org</a>><br class="">Content-Type: text/plain; charset=us-ascii<br class=""><br class="">On Tue, Apr 13, 2021 at 02:19:46PM -0500, Galaxy Being wrote:<br class=""><br class=""><blockquote type="cite" class="">Your answers seem to originate outside of normal Haskell tutorials. Where<br class="">can I start with this higher superset theory?<br class=""></blockquote><br class="">There's a reason why the tutorials don't cover this, the categorical<br class="">foundations of Haskell types are not beginner material. It is perhaps<br class="">best to defer going down this rabbit hole until you're more comfortable<br class="">with the Haskell generally.<br class=""><br class="">You could start with:<br class=""><br class=""> <a href="https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/" class="">https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/</a><br class=""> <a href="https://bartoszmilewski.com/2015/04/07/natural-transformations/" class="">https://bartoszmilewski.com/2015/04/07/natural-transformations/</a><br class=""><br class="">For the Yoneda Lemma specifically, I'd recommend:<br class=""><br class=""> <a href="http://blog.sigfpe.com/2006/11/yoneda-lemma.html" class="">http://blog.sigfpe.com/2006/11/yoneda-lemma.html</a><br class=""><br class="">Parametricity is covered in "Theorems for free":<br class=""><br class=""> <a href="https://www2.cs.sfu.ca/CourseCentral/831/burton/Notes/July14/free.pdf" class="">https://www2.cs.sfu.ca/CourseCentral/831/burton/Notes/July14/free.pdf</a><br class=""><br class="">but it is by no means elementary, though skimming it for the essential<br class="">facts and skipping the gory details is not too difficult.<br class=""><br class="">You could also read "Categories for the Working Mathematician" by<br class="">Saunders Mac Lane.<br class=""></div></div></blockquote></div><br class=""></body></html>