Confusing Terms

Morphism: Structure preserving map.
Homomorphism: Morphism.
Isomorphism: Morphism with inverse.
Endomorphism: Morphism with identical source and target.
Automorphism: Morphism with inverse and with identical source and target.

Homeomorphism : Isomorphism between topological spaces.
Diffeomorphism: Isomorphism between smooth manifolds.

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