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Results tagged with examples
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user 2330
For questions requesting examples of a certain structure or phenomenon
29
votes
3
answers
7k
views
Non finitely-generated subalgebra of a finitely-generated algebra
Ok, I feel a little bit ashamed by my question.
This afternoon in the train, I looked for a counter-example:
— $k$ a field
— $A$ a finitely generated $k$-algebra
— $B$ a $k$-subalgebra of $A$ that …
20
votes
6
answers
3k
views
Is a functor which has a left adjoint which is also its right adjoint an equivalence ?
I am looking for a counter-example of two functors F : C -> D and G : D->C such that
1) F is left adjoint to G
2) F is right adjoint to G
3) F is not an equivalence (ie F is not a quasi-inverse of …
- 1,320
15
votes
Accepted
Is a functor which has a left adjoint which is also its right adjoint an equivalence ?
The answer of Ben Webster, can be made easier. Consider the functor F : (A-mod) -> (A-mod) which maps any A-module on (0). Then, F is a left adjoint to F ; and so, is a also a right adjoint to F. This …
- 1,320