In many toposes, the subobject classifier identifies which subobjects of an object correspond to characteristic morphisms into it.

In any topos, a subobject is uniquely determined by its classifying morphism to the subobject classifier, and the subobject is the pullback, along this morphism, of the "true" global element of the subobject classifier.

The seminar examined classifying morphisms arising from moduli problems and their role in parameterizing families of objects.

The research team evaluated several subset classifiers on a new biological dataset to determine which model generalized best.

In topos theory, subobject classifiers play a central role in characterizing monomorphisms.