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
Example: Hochschild cohomology of a poset
Let P be a poset. We have HH ∗ (kP) ∼ = H ∗ (P; k)
(Gerstenhaber-Shack). When P = x α →y, the triple
τ : F (P) → P e becomes
(α,1 x )
[1 x ]
[α] (y, x)
(1 y ,α)
[1 y ]
(α,1 op
x )
(x, x)
(1 x ,α op )
(1 y ,α op )
(α,1 op
y )
(x, y)
Note that
kP(x, x) = k1 x , kP(y, y) = k1 y , kP(y, x) = kα and
kP(x, y) = 0. Moreover Res τ kP = kP ∼ = k.
Fei Xu Finite category algebras
(y, y)