Editing Subobject (section)

==Examples==
{{Category see also|Quotient objects}}

In '''Set''', the [[category of sets]], a subobject of ''A'' corresponds to a [[subset]] ''B'' of ''A'', or rather the collection of all maps from sets [[equipotent]] to ''B'' with [[Image (mathematics)|image]] exactly ''B''. The subobject partial order of a set in '''Set''' is just its subset [[Lattice (order)|lattice]].

In '''Grp''', the [[category of groups]], the subobjects of ''A'' correspond to the [[subgroup]]s of ''A''.

Given a [[partially ordered class]] '''P''' = (''P'', ≤), we can form a category with the elements of ''P'' as objects, and a single arrow from ''p'' to ''q'' iff ''p'' ≤ ''q''. If '''P''' has a greatest element, the subobject partial order of this greatest element will be '''P''' itself. This is in part because all arrows in such a category will be monomorphisms.

A subobject of a [[terminal object]] is called a [[subterminal object]].