From: Jim Pryor <profjim@jimpryor.net>
Date: Tue, 2 Nov 2010 15:04:43 +0000 (-0400)
Subject: cat theory tweaks
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=11012fa5398867d3f2c08b40912b0b85aa710c75

cat theory tweaks

Signed-off-by: Jim Pryor <profjim@jimpryor.net>
---

diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index d5c55d65..e596c31d 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -255,6 +255,21 @@ Similarly, if <code>&rho;</code> is a natural transformation from `1C` to `MR'`,
 
 where as we said <code>&gamma;</code> is a natural transformation from `G` to some `MR'G`.
 
+Summarizing then, the monad laws can be expressed as:
+
+<pre>
+	For all &gamma;, &phi; in T for which &gamma; <=< &phi; is defined:
+
+	    (i) &gamma; <=< &phi; is also in T
+
+	   (ii) (&rho; <=< &gamma;) <=< &phi;  =  &rho; <=< (&gamma; <=< &phi;)
+
+	(iii.1) (unit G') <=< &gamma;  =  &gamma;
+	        when &gamma; is a natural transformation from some FG' to MG'
+
+	(iii.2) &gamma;  =  &gamma; <=< (unit G)
+	        when &gamma; is a natural transformation from G to some MR'G
+</pre>