Essentially surjective functor

A much surjective functor is a term from the mathematical branch of category theory.

Definition

A functor between two categories and is called essentially surjective (or close ) if for every object exists in an object, so that is isomorphic to.

Examples

• Each equivalence of categories provides a much surjective functor, because a functor is an equivalence if and only if it is fully faithful and essentially surjective.
• Conversely, the essential surjectivity also be characterized by equivalence: A functor is surjective if and only essential if the to is the image of the objects produced in full subcategory of equivalent.
• If a body is, the category of vector spaces (in the sense of the times the direct sum ), cardinal number, and the category of all vector spaces, then the embedding essentially surjective, because according to the results of linear algebra is any vector space is isomorphic to a.
• Is the field of real or complex numbers, the category of Hilbert spaces, so is the isometric isomorphisms and the category of sets with the bijective pictures by the theorem of Fischer- Riesz functor much surjective.