From cf067fa0afa70fa0a9c3c9c4a04a39d078afda87 Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Tue, 2 Nov 2010 08:07:54 -0400 Subject: [PATCH] cat theory tweaks Signed-off-by: Jim Pryor --- advanced_topics/monads_in_category_theory.mdwn | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) 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 1E, which is such that for every morphism `f:C1->C2`: 1C2 o f = f = f o 1C1
+	(iii) every element E of the category has to have an identity morphism 1E, which is such that for every morphism f:C1->C2: 1C2 o f = f = f o 1C1
```
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