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=588d1a30f237dcad0f82b0a26d875af84b9459da;hp=33f9bf3894a72046eaeb169d8c2aacd45b155211;hb=c0a6070f7c11da38419b5e5da90afeddc6520b95;hpb=d752bea8fab7d8a83e1704ca99d37dd5dfcc52f3
diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index 33f9bf38..588d1a30 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -258,23 +258,23 @@ where as we said γ
is a natural transformation from `G` to so
Summarizing then, the monad laws can be expressed as:
- For all γ, φ in T for which ρ <=< γ and γ <=< φ are defined: + For all ρ, γ, φ in T for which ρ <=< γ and γ <=< φ are defined: - (i) γ <=< φ is also in T + (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) + (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 `<=<`.