nLab
module over a groupoid

Contents

Idea

A module over a groupoid is a collection of abelian groups equipped with a linear action by a groupoid.

Definition

Definition

(module over a groupoid)

Let 𝒢=(𝒢 1𝒢)\mathcal{G} = (\mathcal{G}_1 \stackrel{\to}{\to} \mathcal{G}) be a groupoid. A module over the groupoid 𝒢\mathcal{G} is a collection {N x} x𝒢 0\{N_x\}_{x \in \mathcal{G}_0} of abelian groups equipped with a collection of maps

N x×𝒢(x,y)N y N_x \times \mathcal{G}(x,y) \to N_y

that are linear and respect the groupoid composition in the obvious way.

References

Created on July 14, 2010 15:16:51 by Urs Schreiber (87.212.203.135)