my beamer presentation - Departament de matemà tiques
my beamer presentation - Departament de matemà tiques
my beamer presentation - Departament de matemà tiques
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Outline<br />
Definitions and examples<br />
Homological properties of kC-mod<br />
An example<br />
A closed symmetric monoidal category<br />
Adjoint functors and a spectral sequence<br />
Two categorical constructions<br />
Hochschild cohomology<br />
Right Kan extension and internal hom<br />
Let M, N ∈ kC-mod. Then M ⊗ N is a kC ⊗ kC-module.<br />
M ˆ⊗N = Res ∆ (M ⊗ N) where Res ∆ : kC ⊗ kC-mod<br />
→ kC-mod.<br />
Thus<br />
Hom kC (L ˆ⊗M, N) = Hom kC (Res ∆ (L ⊗ M), N)<br />
∼ = HomkC⊗kC (L ⊗ M, RK ∆ N)<br />
∼ = HomkC (L, Hom kC (M, RK ∆ N)).<br />
The internal hom is hom(M, N) = Hom kC (M, RK ∆ N).<br />
The dual module of M is <strong>de</strong>fined to be hom(M, k).<br />
When C = G is a group, hom(M, N) ∼ = Hom k (M, N).<br />
Fei Xu<br />
Finite category algebras