From: Jim Pryor <profjim@jimpryor.net>
Date: Tue, 2 Nov 2010 16:12:04 +0000 (-0400)
Subject: cat theory tweaks
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=ac47fea0dc57a0f496d14dba80383206397a35f9;hp=a40cca61ecb584096b4e304508c4a2d0d477555e

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 90f77cbe..24670796 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -422,7 +422,6 @@ Finally, we substitute <code>((join G') -v- (M &gamma;) -v- &phi;)</code> for <c
 	==>
 			 (unit G') is a transformation from G' to MG', so:
 			 (unit G') <=< &gamma; becomes: ((join G') (M unit G') &gamma;)
-						    which is: ((join G') (M unit G') &gamma;)
 
 			 substituting in (iii.1), we get:
 			 ((join G') (M unit G') &gamma;) = &gamma;
@@ -439,7 +438,7 @@ Finally, we substitute <code>((join G') -v- (M &gamma;) -v- &phi;)</code> for <c
 	 (iii.2) &gamma;  =  &gamma; <=< (unit G)
 	         when &gamma; is a natural transformation from G to some MR'G
 	==>
-			 unit <=< &gamma; becomes: (join R'G) (M &gamma;) unit
+			 unit <=< &gamma; becomes: ((join R'G) (M &gamma;) unit)
 			
 			 substituting in (iii.2), we get:
 			 &gamma; = ((join R'G) (M &gamma;) (unit G))
@@ -457,8 +456,12 @@ Finally, we substitute <code>((join G') -v- (M &gamma;) -v- &phi;)</code> for <c
 
 Collecting the results, our monad laws turn out in this format to be:
 
-</pre>
-	when &phi; a transformation from F to MF', &gamma; a transformation from F' to MG', &rho; a transformation from G' to MR' are all in T:
+<pre>
+	For all &rho;, &gamma;, &phi; in T,
+	where &phi; is a transformation from F to MF',
+	&gamma; is a transformation from G to MG',
+	&rho; is a transformation from R to MR',
+	and F'=G and G'=R:
 
 	    (i') ((join G') (M &gamma;) &phi;) etc also in T