From 37c4d3dde1f5d08f4913080b1e232248469d0077 Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Tue, 2 Nov 2010 10:57:10 -0400 Subject: [PATCH 1/1] cat theory tweaks Signed-off-by: Jim Pryor --- advanced_topics/monads_in_category_theory.mdwn | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) 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) -- 2.11.0