cat theory tweaks

[lambda.git] / advanced_topics / monads_in_category_theory.mdwn

diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index 8c5f4cd..078bec2 100644 (file)
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -82,12 +82,11 @@ A **functor** is a "homomorphism", that is, a structure-preserving mapping, betw
 <pre>
          (i) associate with every element C1 of <b>C</b> an element F(C1) of <b>D</b>
 
-        (ii) associate with every morphism f:C1&rarr;C2 of <b>C</b> a morphism
-             F(f):F(C1)&rarr;F(C2) of <b>D</b>
+        (ii) associate with every morphism f:C1&rarr;C2 of <b>C</b> a morphism F(f):F(C1)&rarr;F(C2) of <b>D</b>
 
        (iii) "preserve identity", that is, for every element C1 of <b>C</b>:
-             F of C1's identity morphism in <b>C</b> must be the identity morphism
-                 of F(C1) in <b>D</b>: F(1<sub>C1</sub>) = 1<sub>F(C1)</sub>.
+             F of C1's identity morphism in <b>C</b> must be the identity morphism of F(C1) in <b>D</b>:
+             F(1<sub>C1</sub>) = 1<sub>F(C1)</sub>.
 
         (iv) "distribute over composition", that is for any morphisms f and g in <b>C</b>:
              F(g &#8728; f) = F(g) &#8728; F(f)