Editing Subobject (section)

==Interpretation==
This definition corresponds to the ordinary understanding of a subobject outside category theory.   When the category's objects are sets (possibly with additional structure, such as a group structure) and the morphisms are set functions (preserving the additional structure), one thinks of a monomorphism in terms of its image.  An equivalence class of monomorphisms is determined by the image of each monomorphism in the class; that is, two monomorphisms ''f'' and ''g'' into an object ''T'' are equivalent if and only if their images are the same subset (thus, subobject) of ''T''.   In that case there is the isomorphism <math>g^{-1} \circ f</math> of their domains under which corresponding elements of the domains map by ''f'' and ''g'', respectively, to the same element of ''T''; this explains the definition of equivalence.