closed immersion

A morphism of schemes f:(X,𝒪X)(Y,𝒪Y) is a closed immersionPlanetmathPlanetmath if:

  1. 1.

    As a map of topological spacesMathworldPlanetmath, f:XY is a homeomorphism from X into a closed subset of Y, and

  2. 2.

    the morphism of sheaves 𝒪Y𝒪X associated with f is an epimorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath ( in the category of sheaves.

This notion is the analog of the notion of closed immersion ( in the categoryMathworldPlanetmath of differential manifolds.

Title closed immersion
Canonical name ClosedImmersion
Date of creation 2013-03-22 12:50:21
Last modified on 2013-03-22 12:50:21
Owner djao (24)
Last modified by djao (24)
Numerical id 6
Author djao (24)
Entry type Definition
Classification msc 14A15