Morphism - Examples

Examples

  • In the concrete categories studied in universal algebra (groups, rings, modules, etc.), morphisms are usually homomorphisms. Likewise, the notions of automorphism, endomorphism, epimorphism, homeomorphism, isomorphism, and monomorphism all find use in universal algebra.
  • In the category of topological spaces, morphisms are continuous functions and isomorphisms are called homeomorphisms.
  • In the category of smooth manifolds, morphisms are smooth functions and isomorphisms are called diffeomorphisms.
  • In the category of small categories, functors can be thought of as morphisms.
  • In a functor category, the morphisms are natural transformations.

For more examples, see the entry category theory.

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