Mathlib Map

Theorems · Definition · ring theory

Unitary.map

{R : Type u_2} →
  {S : Type u_3} →
    [inst : Monoid R] →
      [inst_1 : StarMul R] → [inst_2 : Monoid S] → [inst_3 : StarMul S] → (R →⋆* S) → ↥(unitary R) →⋆* ↥(unitary S)

The star monoid homomorphism between unitary subgroups induced by a star monoid homomorphism of the underlying star monoids.

Defined in
Mathlib.Algebra.Star.Unitary
Cited by
10 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
MonoidStarMulMonoidStarMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Unitary.mapEquiv · cited by 6Unitary.mapEquivUnitary.mapEquiv_apply · cited by 0Unitary.mapEquiv_applyUnitary.toMonoidHom_mapEquiv · cited by 0Unitary.toMonoidHom_mapEq…Unitary.mapEquiv_symm_apply · cited by 0Unitary.mapEquiv_symm_app…Unitary.toUnits_comp_map · cited by 0Unitary.toUnits_comp_mapUnitary.map_coe · cited by 0Unitary.map_coeUnitary.map_comp · cited by 0Unitary.map_compUnitary.map_id · cited by 0Unitary.map_idUnitary.map_injective · cited by 0Unitary.map_injectiveUnitary.coe_map · cited by 0Unitary.coe_mapUnitary.coe_map_star · cited by 0Unitary.coe_map_starDFunLike.coe · cited by 62936DFunLike.coeMonoid · cited by 3887MonoidSubmonoid · cited by 3086Submonoidunitary · cited by 207unitaryStarMul · cited by 195StarMulSubtype.map · cited by 52Subtype.mapStarMonoidHom · cited by 35StarMonoidHomUnitary.mapCITED BYCITES

Cites7

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

Cited by11

Results whose statement or proof uses this declaration.