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Theorems · Definition · group theory

MulHom.domRestrict

{M : Type u_1} →
  {σ : Type u_4} →
    [inst : Mul M] →
      {N : Type u_5} →
        [inst_1 : Mul N] → [inst_2 : SetLike σ M] → [inst_3 : MulMemClass σ M] → (M →ₙ* N) → (S : σ) → ↥S →ₙ* N

Restriction of a semigroup hom to a subsemigroup of the domain.

Defined in
Mathlib.Algebra.Group.Subsemigroup.Operations
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
MulMulSetLikeMulMemClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MulHom.domRestrict_apply · cited by 1MulHom.domRestrict_applyMulHom.restrict · cited by 0MulHom.restrictMulHom.restrict_apply · cited by 0MulHom.restrict_applySetLike · cited by 1084SetLikeMulHom · cited by 299MulHomMulHom.comp · cited by 44MulHom.compMulMemClass · cited by 25MulMemClassMulMemClass.subtype · cited by 5MulMemClass.subtypeMulHom.domRestrictCITED BYCITES

Cites5

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

Cited by3

Results whose statement or proof uses this declaration.