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Theorems · Definition · ring theory

AddOpposite.opEquiv

{α : Type u_1} → α ≃ αᵃᵒᵖ

The canonical bijection between α and αᵃᵒᵖ.

Defined in
Mathlib.Algebra.Opposites
Cited by
20 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

DomAddAct.mk · cited by 36DomAddAct.mkAddOpposite.opHomeomorph · cited by 13AddOpposite.opHomeomorphAddMonoidAlgebra.opRingEquiv · cited by 6AddMonoidAlgebra.opRingEq…AddOpposite.opAddEquiv · cited by 6AddOpposite.opAddEquivAddOpposite.opMulEquiv · cited by 5AddOpposite.opMulEquivAddSubgroup.equivOp · cited by 5AddSubgroup.equivOpAddOpposite.opEquiv_apply · cited by 5AddOpposite.opEquiv_applyisAddLeftRegular_op · cited by 4isAddLeftRegular_opAddMonoidAlgebra.opRingEquiv_apply · cited by 3AddMonoidAlgebra.opRingEq…Polynomial.opRingEquiv_op_monomial · cited by 3Polynomial.opRingEquiv_op…isAddRightRegular_op · cited by 3isAddRightRegular_opAddEquiv.neg' · cited by 3AddEquiv.neg'AddOpposite.opEquiv_symm_apply · cited by 2AddOpposite.opEquiv_symm_…AddSubsemigroup.equivOp · cited by 2AddSubsemigroup.equivOpPolynomial.coeff_opRingEquiv · cited by 2Polynomial.coeff_opRingEq…Equiv · cited by 8337EquivAddOpposite · cited by 452AddOppositeAddOpposite.op · cited by 192AddOpposite.opAddOpposite.unop · cited by 125AddOpposite.unopAddOpposite.op_unop · cited by 1AddOpposite.op_unopAddOpposite.unop_op · cited by 1AddOpposite.unop_opAddOpposite.opEquivCITED BYCITES

Cites6

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

Cited by32

Results whose statement or proof uses this declaration.