Theorems · Definition · group theory
Submonoid.centerToMulOpposite
{M : Type u_2} → [inst : MulOneClass M] → ↥(Submonoid.center M) ≃* ↥(Submonoid.center Mᵐᵒᵖ)The center of a monoid is isomorphic to the center of its opposite.
- Defined in
- Mathlib.GroupTheory.Submonoid.Center
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClass
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.
- Submonoidstatement · cited by 3,086
- MulEquivstatement · cited by 1,142
- MulOppositestatement · cited by 1,135
- MulOneClassstatement and proof · cited by 1,018
- Submonoid.centerstatement · cited by 24
- Subsemigroup.centerToMulOppositeproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.centerToMulOppositeproof · cited by 2
- Submonoid.centerToMulOpposite_apply_coestatement and proof · cited by 0
- Submonoid.centerToMulOpposite_symm_apply_coestatement and proof · cited by 0