Difference between revisions of "Fiber product"

(New page: The '''fiber product''', also called the '''pullback''' is an idea in category theory which occurs in many areas of mathematics. == Definition == Let <math>X</math>, <math>Y</math>, ...)
 
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The '''fiber product''', also called the '''pullback''' is an idea in [[category theory]] which occurs in many areas of mathematics.
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The '''fiber product''', also called the '''pullback''', is an idea in [[category theory]] which occurs in many areas of mathematics.
  
 
== Definition ==
 
== Definition ==

Revision as of 21:20, 28 May 2008

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 $\phi(x) = \psi(y)$.

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