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

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

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

References

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