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=8552e65ebcd724a1ed691b199074f417f9e9adde;hp=4941e80b99875eb3f9179c704da83e63d4d3ae66;hb=7f6da341406e8d94c17b2093473b0a37863efcc0;hpb=4f87cdd50334c5d9dddbdad136fac4008d8ce6ff
diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index 4941e80b..8552e65e 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -212,9 +212,7 @@ 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.
-
-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:
(i) γ <=< φ is also in T
@@ -351,7 +349,7 @@ So our **(lemma 2)** is:
-Finally, we substitute ((join G') -v- (M γ) -v- φ) for γ <=< φ in the monad laws. For simplicity, I'll omit the "-v-".
+Finally, we substitute ((join G') -v- (M γ) -v- φ) for γ <=< φ in the monad laws. For simplicity, I'll omit the "-v-".
for all φ,γ,ρ in T, where φ is a transformation from F to MF', γ is a transformation from G to MG', R is a transformation from R to MR', and F'=G and G'=R: