cat theory tweaks

Signed-off-by: Jim Pryor <profjim@jimpryor.net>

diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index 3ec8fea..aef5538 100644 (file)
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -73,10 +73,12 @@ 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:
 
 --------
 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:
 

+<pre>

        (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(1<sub>C1</sub>) = 1<sub>F(C1)</sub>.
        (iv) "distribute over composition", that is for any morphisms f and g in **C**: F(g o f) = F(g) o 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(1<sub>C1</sub>) = 1<sub>F(C1)</sub>.
        (iv) "distribute over composition", that is for any morphisms f and g in **C**: F(g o f) = F(g) o F(f)

+</pre>

 
 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`.
 
 
 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`.