nLab cobase change

Definition

Cobase change is another term for pushout of a morphism:

if

$$\array{ X &\to & U \\ \downarrow && \downarrow \\ Y &\to& Y \sqcup_X U }$$

is a pushout square in some category then the morphism $U \to U \sqcup_X Y$ is the cobase change or cobase extension of $X \to Y$ along $X \to U$.

Related concepts

• The dual concept is base change.

• base change

• homotopy co-base change?