my beamer presentation - Departament de matemà tiques

Outline
Definitions and examples
Homological properties of kC-mod
An example
B. Mitchell’s theorem
Finite categories and their algebras
Representations and modules
Motivation
Given a finite category algebra kC, we are interested in
the homological properties of kC-mod of finitely
generated left kC-modules.
Let Vect k be the category of finite-dimensional k-vector
spaces, and Vectk
C the category of covariant functors.
Each functor is called a k-representation of C.
Mitchell’s Theorem: kC-mod ∼ = Vect C k .
It simply says that each kC-module corresponds uniquely
to a k-representation of C, and vice versa.
F ↦→ ⊕ x∈Ob C F (x) and M ↦→ F M such that
F M (x) = 1 x · M.
Fei Xu
Finite category algebras