<p>'''Definition 1.3.''' A ''functor'' <math>F : \mathcal{A} \to \mathcal{B}</math> is first of all a morphism of graphs …, that is, it sends objects of <math>\mathcal{A}</math> to objects of <math>\mathcal{B}</math> and arrows of <math>\mathcal{A}</math> to arrows of <math>\mathcal{B}</math> such that, if <math>f : A \to A',</math> then <math>F(f) : F(A) \to F(A').</math> Moreover, a functor preserves identities and composition; thus:</p> | <p>'''Definition 1.3.''' A ''functor'' <math>F : \mathcal{A} \to \mathcal{B}</math> is first of all a morphism of graphs …, that is, it sends objects of <math>\mathcal{A}</math> to objects of <math>\mathcal{B}</math> and arrows of <math>\mathcal{A}</math> to arrows of <math>\mathcal{B}</math> such that, if <math>f : A \to A',</math> then <math>F(f) : F(A) \to F(A').</math> Moreover, a functor preserves identities and composition; thus:</p> |