A power object of an object 
in a category 
is an object 
equipped with a subobject 
of 
such that every subobject 
of 
is obtained as a pullback
of 
along 
for a unique morphism 
. Power objects generalize
power sets from the category
of sets. A category with finite limits
and power objects is a topos.
Power Object
See also
Category, Power Set, Pullback, Subobject, ToposExplore with Wolfram|Alpha
References
Mac Lane, S. and Moerdijk, I. Sheaves in Geometry and Logic: A First Introduction to Topos Theory. New York: Springer, 1994.Cite this as:
Weisstein, Eric W. "Power Object." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PowerObject.html