---
advanced_topics/monads_in_category_theory.mdwn | 15 +++++++++++----
1 file changed, 11 insertions(+), 4 deletions(-)
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(1_{C1}) = 1_{F(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(1_{C1}) = 1_{F(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`.
--
2.11.0