fact: Definition axioms f := let a := source f in let b := target f in (Umorphism.like f) & (Category.axioms a) & (Category.axioms b) & (forall x, ob a x -> ob b (fob f x)) & (forall x, ob a x -> id b (fob f x) = fmor f (id a x)) & (forall u, mor a u -> mor b (fmor f u)) & (forall u, mor a u -> source (fmor f u) = fob f (source u)) & (forall u, mor a u -> target (fmor f u) = fob f (target u)) & (forall u v, mor a u -> mor a v -> source u = target v -> comp b (fmor f u) (fmor f v) = fmor f (comp a u v)).
imports: Arith category