A subobject of an object 
in a category is an equivalence
class of monomorphisms 
. Two such monomorphisms 
and 
represent the same subobject if there is an isomorphism 
such that 
. The subobjects of 
form a partially ordered
set under factorization.
Subobject
See also
Category, Isomorphism, Monomorphism, Object, Power Object, Subterminal ObjectExplore with Wolfram|Alpha
References
Mac Lane, S. Categories for the Working Mathematician, 2nd ed. New York: Springer-Verlag, 1998.Cite this as:
Weisstein, Eric W. "Subobject." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Subobject.html