closed immersion
A morphism of schemes $f:(X,{\mathcal{O}}_{X})\u27f6(Y,{\mathcal{O}}_{Y})$ is a closed immersion^{} if:

1.
As a map of topological spaces^{}, $f:X\u27f6Y$ is a homeomorphism from $X$ into a closed subset of $Y$, and

2.
the morphism of sheaves ${\mathcal{O}}_{Y}\u27f6{\mathcal{O}}_{X}$ associated with $f$ is an epimorphism^{} (http://planetmath.org/AbelianCategory) in the category of sheaves.
This notion is the analog of the notion of closed immersion (http://planetmath.org/Immersion) in the category^{} of differential manifolds.
Title  closed immersion 

Canonical name  ClosedImmersion 
Date of creation  20130322 12:50:21 
Last modified on  20130322 12:50:21 
Owner  djao (24) 
Last modified by  djao (24) 
Numerical id  6 
Author  djao (24) 
Entry type  Definition 
Classification  msc 14A15 