---
advanced_topics/monads_in_category_theory.mdwn | 14 ++++++++------
1 file changed, 8 insertions(+), 6 deletions(-)
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 1_{E}, which is such that for every morphism
- f:C1→C2: 1_{C2} ∘ f = f = f ∘ 1_{C1}
+ morphism 1_{E}, which is such that for every morphism
+ f:C1→C2: 1_{C2} ∘ f = f = f ∘ 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.
--
2.11.0