As nouns the difference between codomain and subobject

is that codomain is (mathematics) the target space into which a function maps elements of its domain it always contains the range of the function, but can be larger than the range if the function is not surjective while subobject is (category theory) given an object b'', a ''subobject'' of it is an equivalence class of objects $a\_i$ which relate to ''b'' through monomorphisms $m\_i\; :\; a\_i\; \backslash rightarrow\; b$ (if a pair of monomorphisms with codomain ''b'' , which is a monomorphism) of another set.