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Theorems · Definition · group theory

Subsemigroup.op

{M : Type u_2} → [inst : Mul M] → Subsemigroup M → Subsemigroup Mᵐᵒᵖ

Pull a subsemigroup back to an opposite subsemigroup along MulOpposite.unop

Defined in
Mathlib.Algebra.Group.Subsemigroup.MulOpposite
Cited by
28 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
Mul
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Around this declaration

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

Subsemigroup.opEquiv · cited by 18Subsemigroup.opEquivSubsemigroup.op_injective · cited by 2Subsemigroup.op_injectiveSubsemigroup.equivOp · cited by 2Subsemigroup.equivOpSubsemigroup.op_bot · cited by 1Subsemigroup.op_botSubsemigroup.op_closure · cited by 1Subsemigroup.op_closureSubsemigroup.op_inj · cited by 1Subsemigroup.op_injSubsemigroup.op_sInf · cited by 1Subsemigroup.op_sInfSubsemigroup.op_top · cited by 1Subsemigroup.op_topSubsemigroup.op_unop · cited by 1Subsemigroup.op_unopSubsemigroup.unop_op · cited by 0Subsemigroup.unop_opSubsemigroup.unop_sInf · cited by 0Subsemigroup.unop_sInfSubsemigroup.unop_sSup · cited by 0Subsemigroup.unop_sSupSubsemigroup.opEquiv_apply · cited by 0Subsemigroup.opEquiv_applySubsemigroup.op_eq_bot · cited by 0Subsemigroup.op_eq_botSubsemigroup.op_eq_top · cited by 0Subsemigroup.op_eq_topSetLike.coe · cited by 8199SetLike.coeSet.preimage · cited by 4946Set.preimageMulOpposite · cited by 1135MulOppositeSubsemigroup · cited by 323SubsemigroupMulOpposite.unop · cited by 268MulOpposite.unopSubsemigroup.opCITED BYCITES

Cites5

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

Cited by30

Results whose statement or proof uses this declaration.