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Summary: Ring epimorphisms and tilting theory
Lidia Angeleri H¨ugel
Plan:
1. Reminder on adjoint functors
2. Ring epimorphisms
3. Universal localization
4. Homological epimorphisms
5. Tilting modules and recollements
6. Tilting modules arising from ring epimorphisms
7. Classification of tilting modules
1. Reminder on adjoint functors
Two functors q : C D, i : D C between preadditive categories
C, D form an adjoint pair (q, i) if for any C C, D D there is a
natural iso
HomD(q(C), D) = HomC(C, i(D))
Then there are natural morphisms
: IdC iq unit (choose D = q(C) and set 1q(C) C )
: qi IdD counit (choose C = i(D) and set D 1i(D))
such that
q(C)
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