morphism of schemes induces a map of points

Let f:XY be a morphism of schemes over S, and let T be a particular scheme over S. Then f induces a natural function from the S-points of X to the S-points of T.

Recall that a T-point of X is a morphism ϕ:TX. So examine the following diagram:


Since all the schemes in question are S-schemes, the solid arrows all commute. The dashed arrow ψ we simply construct as fϕ, making the whole diagram commute. The ψ is a T-point of Y.

Title morphism of schemes induces a map of points
Canonical name MorphismOfSchemesInducesAMapOfPoints
Date of creation 2013-03-22 14:11:02
Last modified on 2013-03-22 14:11:02
Owner archibal (4430)
Last modified by archibal (4430)
Numerical id 4
Author archibal (4430)
Entry type Result
Classification msc 14A15