nLab module over a groupoid

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

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

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

References

• Ronnie Brown, Philip Higgins, Rafael Sivera, Nonabelian Algebraic Topology