Theorems · Definition · group theory
DistribMulAction.toAddEquiv
{G : Type u_1} → (A : Type u_3) → [inst : Group G] → [inst_1 : AddMonoid A] → [DistribMulAction G A] → G → A ≃+ AEach element of the group defines an additive monoid isomorphism.
This is a stronger version of MulAction.toPerm.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- AddMonoidHomproof · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- Equiv.Permproof · cited by 1,375
- AddEquivstatement · cited by 1,087
- DistribMulActionstatement and proof · cited by 584
- Equiv.invFunproof · cited by 163
- ZeroHom.toFunproof · cited by 101
- Equiv.right_invproof · cited by 68
- AddMonoidHom.toZeroHomproof · cited by 61
- Equiv.left_invproof · cited by 59
Cited by6
Results whose statement or proof uses this declaration.
- MulSemiringAction.toRingEquivproof · cited by 13
- DistribMulAction.toLinearEquivproof · cited by 8
- DistribMulAction.toAddAutproof · cited by 1
- DistribMulAction.toAddAut_applystatement · cited by 0
- DistribMulAction.toAddEquiv_applystatement and proof · cited by 0
- DistribMulAction.toAddEquiv_symm_applystatement and proof · cited by 0