my beamer presentation - Departament de matemà tiques

Outline
Definitions and examples
Homological properties of kC-mod
An example
A closed symmetric monoidal category
Adjoint functors and a spectral sequence
Two categorical constructions
Hochschild cohomology
Theorem
For any M ∈ kC e -mod,
Ext ∗ kC e(kC, M) ∼ = Ext ∗ kF (C)(k, Res τ M);
For any N ∈ kC-mod, Ext ∗ kC(k, N) ∼ = Ext ∗ kF (C)(k, Res t N);
The module kC ∈ kC e -mod restricts to
Res τ kC ∼ = k ⊕ U ∈ kF (C)-mod;
There exists a natural split surjective ring homomorphism
Ext ∗ kC e(kC, kC) → Ext∗ kC(k, k) ∼ = Ext ∗ kF (C)(k, k).
We can understand Hochschild cohomology via ordinary
cohomology.
Fei Xu
Finite category algebras