cat theory tweaks

[lambda.git] / advanced_topics / monads_in_category_theory.mdwn

diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index d5c55d6..33f9bf3 100644 (file)
--- 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 &rho; <=< &gamma; and  &gamma; <=< &phi; are 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>