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=3ec8feaaf209c5ebf7e4f125aaa6f312abd6bb07;hp=37976ea28b64ac87fbdd804a821760168497cc36;hb=cf067fa0afa70fa0a9c3c9c4a04a39d078afda87;hpb=c801371a433f178c07249aef38b74b7e38347280
diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index 37976ea2..3ec8feaa 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -45,9 +45,9 @@ When a morphism `f` in category **C** has source `C1` and target `C2`, we'll wri
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 o f` is also a morphism of the category, which maps `C1->C3`.
+ (i) the class of morphisms has to be closed under composition: where f:C1->C2 and g:C2->C3, g o 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 1_{E}, which is such that for every morphism `f:C1->C2`: 1_{C2} o f = f = f o 1_{C1}
+ (iii) every element E of the category has to have an identity morphism 1_{E}, which is such that for every morphism f:C1->C2: 1_{C2} o f = f = f o 1_{C1}

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.