Editing Pushout (category theory) (section)

{{Short description|Most general completion of a commutative square given two morphisms with same domain}}
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 (category theory)|diagram]] consisting of two [[morphism]]s ''f'' : ''Z'' &rarr; ''X'' and ''g'' : ''Z'' &rarr; ''Y'' with a common [[Domain of a function|domain]]. The pushout consists of an [[object (category theory)|object]] ''P'' along with two morphisms ''X'' &rarr; ''P''  and ''Y'' &rarr; ''P'' that complete a [[commutative diagram|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. Common notations for the pushout are <math>P = X \sqcup_Z Y</math> and <math>P = X +_Z Y</math>.

The pushout is the [[dual (category theory)|categorical dual]] of the [[pullback (category theory)|pullback]].