nLab
cobase change
Context
Limits and colimits
limits and colimits
1Categorical

limit and colimit

limits and colimits by example

commutativity of limits and colimits

small limit

filtered colimit

sifted colimit

connected limit, wide pullback

preserved limit, reflected limit, created limit

product, fiber product, base change, coproduct, pullback, pushout, cobase change, equalizer, coequalizer, join, meet, terminal object, initial object, direct product, direct sum

finite limit

Kan extension

weighted limit

end and coend
2Categorical
(∞,1)Categorical
Modelcategorical
Contents
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 $X \to U$.