A functor is corepresentable if it is (isomorphic to) a functor of the form for some object .
This is equivalently a representable functor defined on the opposite category . Often no terminological distinction is made between representable and corepresentable ones (both being called simply “representable”), since a functor can only be “corepresentable” while a functor can only be “representable”.
Particularly in the study of moduli problems, there is also the notion of corepresentable contravariant functors. A functor is corepresentable if and only if there exists an object in and a morphism such that for any object in , the canonical map is bijective.
Last revised on June 14, 2020 at 05:45:51. See the history of this page for a list of all contributions to it.