my beamer presentation - Departament de matemà tiques

Outline
Definitions and examples
Homological properties of kC-mod
An example
Finite categories and their algebras
Representations and modules
Motivation
Subgroups as transporter categories
Let G be a finite group and H a subgroup. We consider
the set of left cosets Q := G/H which can be regarded as
a G-poset: G acts via left multiplication.
The transporter category G ⋉ Q is a connected groupoid
whose skeleton is isomorphic to H.
In this way one can recover all subgroups of G, up to
category equivalences.
A category equivalence D → C induces a Morita
equivalence kD ≃ kC (and a homotopy equivalence
BD ≃ BC as well).
The functor G ⋉ Q → G gives rise to the usual
restriction and transfer between H ∗ (G; k) and H ∗ (H; k).
Fei Xu
Finite category algebras