From: Jim Pryor Date: Tue, 2 Nov 2010 13:34:14 +0000 (-0400) Subject: cat theory tweaks X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=0fbb8868c90353ef094c89e096a12f69e54af15b cat theory tweaks Signed-off-by: Jim Pryor --- diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn index c0d4bf7f..2b433d27 100644 --- a/advanced_topics/monads_in_category_theory.mdwn +++ b/advanced_topics/monads_in_category_theory.mdwn @@ -208,9 +208,17 @@ In other words, `<=<` is a binary operator that takes us from two members Now we can specify the "monad laws" governing a monad as follows: +
	
 	(T, <=<, unit) constitute a monoid
+
+ +That's it. Well, there may be a wrinkle here. + +`test` + +I don't know whether the definition of a monoid requires the operation to be defined for every pair in its set. In the present case, γ <=< φ isn't fully defined on `T`, but only when φ is a transformation to some `MF'` and γ is a transformation from `F'`. But wherever `<=<` is defined, the monoid laws are satisfied: -That's it. Well, there may be a wrinkle here. I don't know whether the definition of a monoid requires the operation to be defined for every pair in its set. In the present case, γ <=< φ isn't fully defined on `T`, but only when φ is a transformation to some `MF'` and γ is a transformation from `F'`. But wherever `<=<` is defined, the monoid laws are satisfied: +`test` 
 	    (i) γ <=< φ is also in T