Actions and Homomorphisms
An action of on is equivalent to a homomorphism .
Theorem 4.3
Proof
For an action , define . The inverse of is , and , so is a homomorphism . Conversely, a homomorphism defines an action by ; the identity and associativity axioms follow from the homomorphism identities.
Related
Stated in
- Theorem 4.3§4.1 Introduction