From 50e06b4a50c0fcdc84f5cc94773316935871ceb1 Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Tue, 2 Nov 2010 08:29:02 -0400 Subject: [PATCH] cat theory tweaks Signed-off-by: Jim Pryor --- advanced_topics/monads_in_category_theory.mdwn | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn index 1590619a..7b52c3a6 100644 --- a/advanced_topics/monads_in_category_theory.mdwn +++ b/advanced_topics/monads_in_category_theory.mdwn @@ -24,8 +24,8 @@ A **monoid** is a structure (S,⋆,z) consisting of an associat 
 	for all s1, s2, s3 in S:
-	(i) s1⋆s2 etc are also in S
-	(ii) (s1⋆s2)⋆s3 = s1⋆(s2⋆s3)
+	  (i) s1⋆s2 etc are also in S
+	 (ii) (s1⋆s2)⋆s3 = s1⋆(s2⋆s3)
 	(iii) z⋆s1 = s1 = s1⋆z
@@ -45,15 +45,15 @@ When a morphism `f` in category C has source `C1` and target `C2`, we'll To have a category, the elements and morphisms have to satisfy some constraints: 
-	(i)   the class of morphisms has to be closed under composition:
+	  (i) the class of morphisms has to be closed under composition:
 	      where f:C1→C2 and g:C2→C3, g ∘ f is also a
 	      morphism of the category, which maps C1→C3.
 
-	(ii)  composition of morphisms has to be associative
+	 (ii) composition of morphisms has to be associative
 
 	(iii) every element E of the category has to have an identity
-	      morphism 1E, which is such that for every morphism
-	      f:C1→C2: 1C2 ∘ f = f = f ∘ 1C1
+	      morphism 1E, which is such that for every morphism f:C1→C2:
+	      1C2 ∘ f = f = f ∘ 1C1
These parallel the constraints for monoids. Note that there can be multiple distinct morphisms between an element `E` and itself; they need not all be identity morphisms. Indeed from (iii) it follows that each element can have only a single identity morphism. -- 2.11.0