Let 
be a class of topological spaces that is closed
under homeomorphism, and let 
be a topological space.
If 
and for every 
such that 
,
is a retract
of 
,
then 
is an absolute retract for the class 
.
These notions can be generalized to category theory, and because there are category-theoretic versions, there are also other more specific versions, as in universal algebra and modern algebra.
