X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=advanced_topics%2Fmonads_in_category_theory.mdwn;h=b148fe6e44c4a6f3ef2d8c31f0a2c5f979d94d53;hp=966fc95c7e6994e66ee5e014cb6a93a91a810c04;hb=24506613cb3b7c8e1cbe45a55f29de40d92bdbd3;hpb=f11472452da56243652ffeed1f56b418f6b6c1dd
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 @@ Ifwhere as we saidφ
is a natural transformation from `F` to `M(1C)` and= (join G') -v- (M (unit G')) -v- γ ?? = (unit G') <=< γ +
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`.