Fibered coproduct

In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain. The pushout consists of an object P along with two morphisms X → P and Y → P which complete a commutative square with the two given morphisms f and g. In fact, the defining universal property of the pushout (given below) essentially says that the pushout is the "most general" way to complete this commutative square. A common notation for the pushout is ${\displaystyle P=X\sqcup _{Z}Y}$ or ${\displaystyle P=X+_{Z}Y}$.

The pushout is the categorical dual of the pullback.

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