Agreed! I’ve actually never met somone who suggests it as either a starter or advanced reference e On Wed, Apr 14, 2021 at 8:43 AM Dominic Steinitz wrote:

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.

Dominic Steinitz dominic@steinitz.org http://idontgetoutmuch.org Twitter: @idontgetoutmuch

From: Viktor Dukhovni To: haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] Haskell function composition commutivity? Message-ID: Content-Type: text/plain; charset=us-ascii

On Tue, Apr 13, 2021 at 02:19:46PM -0500, Galaxy Being wrote:

Your answers seem to originate outside of normal Haskell tutorials. Where can I start with this higher superset theory?

There's a reason why the tutorials don't cover this, the categorical foundations of Haskell types are not beginner material. It is perhaps best to defer going down this rabbit hole until you're more comfortable with the Haskell generally.

You could start with:

https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-p... https://bartoszmilewski.com/2015/04/07/natural-transformations/

For the Yoneda Lemma specifically, I'd recommend:

http://blog.sigfpe.com/2006/11/yoneda-lemma.html

Parametricity is covered in "Theorems for free":

https://www2.cs.sfu.ca/CourseCentral/831/burton/Notes/July14/free.pdf

but it is by no means elementary, though skimming it for the essential facts and skipping the gory details is not too difficult.

You could also read "Categories for the Working Mathematician" by Saunders Mac Lane.

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