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Homomorphism

Definition: Let f: Aⁿ -> A and f': Bⁿ -> B. We call h a homomorphism from A to B (with respect to f and f') if we have:

h: A ->^hom(f,f') B : <=>

   h: A -> B /\

   (exists n in N:

      f: Aⁿ -> A /\ f': Bⁿ -> B /\

      (forall x in Aⁿ: h(f(x₀, ..., x_n-1)) = f'(h(x₀), ..., h(x_n-1)))).

An isomorphism is a bijective homomorphism.

h: A ->^iso(f,f') B : <=> h: A ->^hom(f,f') B /\ h: A ->^bijective B.

Author: Wolfgang Schreiner
Last Modification: December 7, 1999