functor in a sentence

Examples

1. This leads to the definition of the Ext functor and the Tor functor.
2. This leads to the definition of the Ext functor and the Tor functor.
3. A cyclic set is a contravariant functor from the cyclic category to sets.
4. Identity of composition of functors is identity functor.
5. A particular case of this happens when a continuous functor admits a left adjoint.
6. More generally, any type of limit is right adjoint to a diagonal functor.
7. Recall that we could also express a sheaf as a special kind of functor.
8. The forgetful functor is very simple : it just ignores all of the operations.
9. Then let F be the free group functor.
10. Swan's theorem asserts that the functor ? is an equivalence of categories.