X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=advanced_topics%2Fmonads_in_category_theory.mdwn;h=078bec2f0e6ace06427b7ed6a7e7e91a1a689f92;hp=8c5f4cd9b256f39c32dccf112098162a5f9fa78e;hb=2889e6d94efdd9a1babf94ff8dda6dbe1ee1e900;hpb=3ca93ad8ccdf0572c3b803b86ea68dd2ad21a5f2 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)