X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?a=blobdiff_plain;f=advanced_topics%2Fmonads_in_category_theory.mdwn;h=1590619a865d902c81862d5f6abdeb5c3d1a1940;hb=22d14fe68168c87b96699431b381ef6dcb816b4e;hp=46c575cccc8671e46f1595239f43d0399792ba95;hpb=b40dafe674003107ac10de2a66c3679b50dd9db2;p=lambda.git diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn index 46c575cc..1590619a 100644 --- a/advanced_topics/monads_in_category_theory.mdwn +++ b/advanced_topics/monads_in_category_theory.mdwn @@ -45,13 +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:
-	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
+	(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
+
 	(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.