| 1. | A functor is an operation on spaces and functions between them.
|
| 2. | This functor is studied and extended in topological K-theory.
|
| 3. | That is, it is left adjoint to the forgetful functor.
|
| 4. | Any functor which is part of an equivalence is essentially surjective.
|
| 5. | In this sense, the diagonal functor acts trivially on arrows.
|
| 6. | We then say that this functor is filtration by representable functors.
|
| 7. | Similar remarks apply to the colimit functor ( which is covariant ).
|
| 8. | The functor which maps a ring to its underlying additive abelian group.
|
| 9. | The fundamental group functor takes products and coproducts to coproducts.
|
| 10. | Mathematicians do not generally need the full adjoint functor concept.
|
मोबाइल