Fiber product

The fiber product, also called the pullback, is an idea in category theory which occurs in many areas of mathematics.

Definition

Let $X$ , $Y$ , and $Z$ be structures of the same species; let $\phi : X \to Z$ and $\psi : Y \to Z$ be homomorphisms of this species of structure. Then the fiber product of $X$ and $Y$ with respect to $Z$ , denoted $X \times_Z Y$ (when the specific functions $\phi$ and $\psi$ are clear) is the set of elements $(x,y)$ in the product $X \times Y$ in which $\phi(x) = \psi(y)$ .

This article is a stub. Help us out by expanding it.

Page

Toolbox

Search

Fiber product

Definition