📝Category

tags

§ Category Theory

Category:

• a class of Objects (ob(C))

  • Objects don’t have any properties

  • Object only exist to mark start/end of morphisms (Category theory is all about morphisms, not objects)

• a class of Morphisms (Arrows) (hom(C))

  • Morphisms have source and target, no other properties

• composition

  • $\forall f : A \to B, \forall g : B \to C, \exists h : A \to C \ni h = g \circ f$

  • $\forall f : A \to B, \forall g : B \to C, \forall h : C \to D, (f \circ g) \circ h = f \circ (g \circ h)$ (associativity)

  • identity morphism

    • $\forall A, \exists id_A : A \to A \ni \forall f : A \to B, id_A \circ f = f$ (left identity)

    • $\forall B, \exists id_B : B \to B \ni \forall f : A \to B, f \circ id_B = f$ (right identity)