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(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>:
- 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)