From: Jim Pryor Date: Tue, 2 Nov 2010 12:33:31 +0000 (-0400) Subject: cat theory tweaks X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=2889e6d94efdd9a1babf94ff8dda6dbe1ee1e900 cat theory tweaks Signed-off-by: Jim Pryor --- diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn index 8c5f4cd9..078bec2f 100644 --- 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
``` 	  (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
+	 (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(1C1) = 1F(C1).
+	      F of C1's identity morphism in C must be the identity morphism of F(C1) in D:
+	      F(1C1) = 1F(C1).

(iv) "distribute over composition", that is for any morphisms f and g in C:
F(g ∘ f) = F(g) ∘ F(f)
```