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=d5c55d65447e6c4890d112a5510f59965a25e349;hp=deb5bace5b8656474b48d69a80d985c9bf5c493d;hb=37c4d3dde1f5d08f4913080b1e232248469d0077;hpb=4bc7f125d288c543b0d22f9f8e69775dc9460317 diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn index deb5bace..d5c55d65 100644 --- a/advanced_topics/monads_in_category_theory.mdwn +++ b/advanced_topics/monads_in_category_theory.mdwn @@ -233,7 +233,8 @@ If φ is a natural transformation from `F` to `M(1C)` and = (((join 1C) G') -v- ((M unit) G') -v- (φ G')) = ((join (1C G')) -v- (M (unit G')) -v- γ) = ((join G') -v- (M (unit G')) -v- γ) - since (unit G') is a natural transformation to MG', this satisfies the definition for <=<: + since (unit G') is a natural transformation to MG', + this satisfies the definition for <=<: = (unit G') <=< γ @@ -247,7 +248,8 @@ Similarly, if ρ is a natural transformation from `1C` to `MR'`, = (((join R') -v- (M ρ) -v- unit) G) = (((join R') G) -v- ((M ρ) G) -v- (unit G)) = ((join (R'G)) -v- (M (ρ G)) -v- (unit G)) - since γ = (ρ G) is a natural transformation to MR'G, this satisfies the definition for <=<: + since γ = (ρ G) is a natural transformation to MR'G, + this satisfies the definition <=<: = γ <=< (unit G)