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Theorems · Definition · group theory

MulEquiv.opOp

(M : Type u_3) → [inst : Mul M] → M ≃* Mᵐᵒᵖᵐᵒᵖ

A monoid is isomorphic to the opposite of its opposite.

Defined in
Mathlib.Algebra.Group.Equiv.Opposite
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses Quot.sound
Assumes
Mul
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Around this declaration

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

RingEquiv.opOp · cited by 6RingEquiv.opOpMulEquiv.opOp_apply · cited by 0MulEquiv.opOp_applyMulEquiv.opOp_symm_apply · cited by 0MulEquiv.opOp_symm_applyRightCancelMonoid.groupOfFinite · cited by 0RightCancelMonoid.groupOf…Equiv · cited by 8337EquivMulEquiv · cited by 1142MulEquivMulOpposite · cited by 1135MulOppositeEquiv.trans · cited by 337Equiv.transMulOpposite.opEquiv · cited by 24MulOpposite.opEquivMulEquiv.opOpCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.