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Morphism of schemes

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Summary

A map of schemes consisting of a continuous map of the underlying spaces and a compatible morphism of structure sheaves that is local on every stalk.

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SchemeMorphism of schemes

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

A scheme morphism adds a continuous map between two schemes and a sheaf homomorphism OYfOX\mathcal O_Y\to f_*\mathcal O_X whose maps on stalks are local ring homomorphisms.

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Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.

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