From: Jim Pryor <profjim@jimpryor.net>
Date: Tue, 2 Nov 2010 12:07:54 +0000 (-0400)
Subject: cat theory tweaks
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=cf067fa0afa70fa0a9c3c9c4a04a39d078afda87;hp=c801371a433f178c07249aef38b74b7e38347280

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 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:
 
 <pre>
-	(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 1<sub>E</sub>, which is such that for every morphism `f:C1->C2`: 1<sub>C2</sub> o f = f = f o 1<sub>C1</sub>
+	(iii) every element E of the category has to have an identity morphism 1<sub>E</sub>, which is such that for every morphism f:C1->C2: 1<sub>C2</sub> o f = f = f o 1<sub>C1</sub>
 </pre>
 
 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.