Theorems · Definition · group theory
MulDistribMulAction.toMulAut
(G : Type u_1) → (M : Type u_2) → [inst : Group G] → [inst_1 : Monoid M] → [MulDistribMulAction G M] → G →* MulAut M
Each element of the group defines a multiplicative monoid isomorphism.
This is a stronger version of MulAction.toPermHom.
- Defined in
- Mathlib.Algebra.Group.Action.End
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement · cited by 3,629
- MulAutstatement · cited by 158
- MulDistribMulActionstatement and proof · cited by 120
- MulDistribMulAction.toMulEquivproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.normalizerMonoidHomproof · cited by 10
- MulAut.conjNormalproof · cited by 9
- mulAutArrowproof · cited by 6
- MulDistribMulAction.toMulAut_applystatement and proof · cited by 0