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