Theorem. is an equivalence relation [isomorphic-equivalence]

    is an equivalence relation: it is

    • Reflexive:
    • Symmetric:
    • Transitive:

    Proof. [#]

      (Reflexivity): Consider an object . Then by .

      (Symmetry): Suppose for some objects . Then there is an isomorphism . Thus by .

      (Transitivity): Suppose . Then there are . Thus by .