Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In algebraic geometry, a proper morphism between schemes is an analogue of a proper map between topological spaces. In mathematics, a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures. The study of morphisms and of the structures (called objects) over which they are defined, is central to category theory. Much of the terminology of morphisms, as well as the intuition underlying them, comes from concrete categories, where the objects are simply sets with some additional structure, and morphisms are structure preserving functions; which articulate relations among various category domains. Because it is a functor which articulates the structure-preserving map between the two categories (algebraic structures), morphisms are not necessarily functions; and objects over which morphisms are defined, are not necessarily sets (see homomorphism).

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