Morphism - Wikipedia: "Examples[edit]
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."
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