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=8c5f4cd9b256f39c32dccf112098162a5f9fa78e;hp=6b2eb805aabd172e15d2e5abf84c90e65ef4b1a0;hb=3ca93ad8ccdf0572c3b803b86ea68dd2ad21a5f2;hpb=6c8379669bdf5f51b58752b190ccc26fe68440af
diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index 6b2eb805..8c5f4cd9 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -80,10 +80,17 @@ Functors
A **functor** is a "homomorphism", that is, a structure-preserving mapping, between categories. In particular, a functor `F` from category C to category D must:
- (i) associate with every element C1 of C an element F(C1) of D
- (ii) associate with every morphism f:C1→C2 of C a morphism F(f):F(C1)→F(C2) of D
- (iii) "preserve identity", that is, for every element C1 of C: F of C1's identity morphism in C must be the identity morphism of F(C1) in D: F(1C1) = 1F(C1).
- (iv) "distribute over composition", that is for any morphisms f and g in C: F(g ∘ f) = F(g) ∘ F(f)
+ (i) associate with every element C1 of C an element F(C1) of D
+
+ (ii) associate with every morphism f:C1→C2 of C a morphism
+ F(f):F(C1)→F(C2) of D
+
+ (iii) "preserve identity", that is, for every element C1 of C:
+ F of C1's identity morphism in C must be the identity morphism
+ of F(C1) in D: F(1C1) = 1F(C1).
+
+ (iv) "distribute over composition", that is for any morphisms f and g in C:
+ F(g ∘ f) = F(g) ∘ F(f)
A functor that maps a category to itself is called an **endofunctor**. The (endo)functor that maps every element and morphism of C to itself is denoted `1C`.