A locally closed immersion factors as a closed immersion followed by an open immersion. Equivalently, it identifies its source with a closed subscheme of an open subscheme of the target.
The diagonal morphism sends a point to the pair consisting of that point twice. Every diagonal of schemes is a locally closed immersion, and a morphism is separated exactly when its diagonal is a closed immersion.

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  1. Morphism of schemes
  2. Scheme
  3. Locally ringed space
  4. Ringed space
  5. Algebraic geometry
  6. Geometry and topology
  7. Area of mathematics
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