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 966fc95..b148fe6 100644 (file)
--- 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 <code>&phi;</code> is a natural transformation from `F` to `M(1C)` and <code>&gamma;</code> is <code>(&phi; G')</code>, that is, a natural transformation from `FG` to `MG`, then we can extend (iii.1) as follows:
 
+<pre>
        &gamma; = (&phi; G')
          = ((unit <=< &phi;) G')
          = ((join -v- (M unit) -v- &phi;) G')
@@ -231,11 +232,13 @@ If <code>&phi;</code> is a natural transformation from `F` to `M(1C)` and <code>
          = (join G') -v- (M (unit G')) -v- &gamma;
          ??
          = (unit G') <=< &gamma;
+</pre>
 
 where as we said <code>&gamma;</code> is a natural transformation from some `FG'` to `MG'`.
 
 Similarly, if <code>&phi;</code> is a natural transformation from `1C` to `MF'`, and <code>&gamma;</code> is <code>(&phi; G)</code>, that is, a natural transformation from `G` to `MF'G`, then we can extend (iii.2) as follows:
 
+<pre>
        &gamma; = (&phi; G)
          = ((&phi; <=< unit) G)
          = (((join F') -v- (M &phi;) -v- unit) G)
@@ -243,6 +246,7 @@ Similarly, if <code>&phi;</code> is a natural transformation from `1C` to `MF'`,
          = ((join F'G) -v- (M (&phi; G)) -v- (unit G))
          ??
          = &gamma; <=< (unit G)
+</pre>
 
 where as we said <code>&gamma;</code> is a natural transformation from `G` to some `MF'G`.