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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
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(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>
<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→C2 of <b>C</b> a morphism
- F(f):F(C1)→F(C2) of <b>D</b>
+ (ii) associate with every morphism f:C1→C2 of <b>C</b> a morphism F(f):F(C1)→F(C2) of <b>D</b>
(iii) "preserve identity", that is, for every element C1 of <b>C</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 ∘ f) = F(g) ∘ F(f)
(iv) "distribute over composition", that is for any morphisms f and g in <b>C</b>:
F(g ∘ f) = F(g) ∘ F(f)