From 24506613cb3b7c8e1cbe45a55f29de40d92bdbd3 Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Tue, 2 Nov 2010 09:14:54 -0400 Subject: [PATCH] cat theory tweaks Signed-off-by: Jim Pryor --- advanced_topics/monads_in_category_theory.mdwn | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn index 966fc95c..b148fe6e 100644 --- a/advanced_topics/monads_in_category_theory.mdwn +++ b/advanced_topics/monads_in_category_theory.mdwn @@ -224,6 +224,7 @@ That's it. Well, there may be a wrinkle here. I don't know whether the definitio If φ is a natural transformation from `F` to `M(1C)` and γ is (φ G'), that is, a natural transformation from `FG` to `MG`, then we can extend (iii.1) as follows: +
 	γ = (φ G')
 	  = ((unit <=< φ) G')
 	  = ((join -v- (M unit) -v- φ) G')
@@ -231,11 +232,13 @@ If φ is a natural transformation from `F` to `M(1C)` and 
 	  = (join G') -v- (M (unit G')) -v- γ
 	  ??
 	  = (unit G') <=< γ
+
where as we said γ is a natural transformation from some `FG'` to `MG'`. Similarly, if φ is a natural transformation from `1C` to `MF'`, and γ is (φ G), that is, a natural transformation from `G` to `MF'G`, then we can extend (iii.2) as follows: +
 	γ = (φ G)
 	  = ((φ <=< unit) G)
 	  = (((join F') -v- (M φ) -v- unit) G)
@@ -243,6 +246,7 @@ Similarly, if φ is a natural transformation from `1C` to `MF'`,
 	  = ((join F'G) -v- (M (φ G)) -v- (unit G))
 	  ??
 	  = γ <=< (unit G)
+
where as we said γ is a natural transformation from `G` to some `MF'G`. -- 2.11.0