X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?a=blobdiff_plain;f=advanced_topics%2Fmonads_in_category_theory.mdwn;h=1d7ede7167c1c9fdeed424ea8925725c30308232;hb=d6f9a31a5eadc6270f0c97d63d9e97f11b5081f5;hp=d5c55d65447e6c4890d112a5510f59965a25e349;hpb=37c4d3dde1f5d08f4913080b1e232248469d0077;p=lambda.git
diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index d5c55d65..1d7ede71 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -255,11 +255,26 @@ Similarly, if ρ
is a natural transformation from `1C` to `MR'`,
where as we said γ
is a natural transformation from `G` to some `MR'G`.
+Summarizing then, the monad laws can be expressed as:
+
+
+ For all ρ, γ, φ in T for which ρ <=< γ and γ <=< φ are defined: + + (i) γ <=< φ etc are also in T + + (ii) (ρ <=< γ) <=< φ = ρ <=< (γ <=< φ) + + (iii.1) (unit G') <=< γ = γ + when γ is a natural transformation from some FG' to MG' + + (iii.2) γ = γ <=< (unit G) + when γ is a natural transformation from G to some MR'G +-The standard category-theory presentation of the monad laws ------------------------------------------------------------ +Getting to the standard category-theory presentation of the monad laws +---------------------------------------------------------------------- In category theory, the monad laws are usually stated in terms of `unit` and `join` instead of `unit` and `<=<`.