nLab
equivariant

Idea

An equivariant function is a homomorphism between two G-sets:

$$f \;\colon\; X \longrightarrow Y \phantom{AAA} f(g \cdot x) = g \cdot f(x) \phantom{A} \forall g \in G \phantom{A} \forall x \in X$$

More generally, an equivariant morphism is a homomorphism of $G$-actions.

Related concepts

• equivariant cohomology

• equivariant homotopy theory

• equivariant stable homotopy theory

References

• Glen Bredon, Section I.2 of: Introduction to compact transformation groups, Academic Press 1972 (ISBN 9780080873596, pdf)