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Theorems · Definition · group theory

SMulCommClass.toMulActionHom

{M : Type u_11} →
  (N : Type u_9) → (α : Type u_10) → [inst : SMul M α] → [inst_1 : SMul N α] → [SMulCommClass M N α] → M → α →ₑ[id] α

If actions of M and N on α commute, then for c : M, (c • · : α → α) is an N-action homomorphism.

Defined in
Mathlib.GroupTheory.GroupAction.Hom
Cited by
1 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
SMulSMulSMulCommClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SMulCommClass.toDistribMulActionHom · cited by 1SMulCommClass.toDistribMu…SMulCommClass.toMulActionHom_apply · cited by 0SMulCommClass.toMulAction…SMulCommClass · cited by 1927SMulCommClassSMulCommClass.smul_comm · cited by 143SMulCommClass.smul_commMulActionHom · cited by 124MulActionHomSMulCommClass.toMulActionHomCITED BYCITES

Cites3

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Cited by2

Results whose statement or proof uses this declaration.