Mathlib Map

Theorems · Theorem · ring theory

StarHomClass.map_star

∀ {F : Type u_1} {R : outParam (Type u_2)} {S : outParam (Type u_3)} {inst : Star R} {inst_1 : Star S}
  {inst_2 : FunLike F R S} [self : StarHomClass F R S] (f : F) (r : R), f (star r) = star (f r)

the maps preserve star

Defined in
Mathlib.Algebra.Star.Basic
Cited by
20 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
StarHomClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

NonUnitalStarAlgHomClass.toNonUnitalStarAlgHom · cited by 23NonUnitalStarAlgHomClass.…StarAlgHomClass.toStarAlgHom · cited by 7StarAlgHomClass.toStarAlg…IsSelfAdjoint.map · cited by 7IsSelfAdjoint.mapcfcₙ_star · cited by 4cfcₙ_starcfc_star · cited by 3cfc_stargelfandTransform_map_star · cited by 2gelfandTransform_map_starCommute.cfcHom · cited by 2Commute.cfcHomCommute.cfcₙHom · cited by 2Commute.cfcₙHomStarAlgEquiv.ofBijective · cited by 2StarAlgEquiv.ofBijectiveStarMonoidHom.ofClass · cited by 1StarMonoidHom.ofClassUnitary.map_mem · cited by 1Unitary.map_memcontinuous_cfcHomSuperset_left · cited by 1continuous_cfcHomSuperset…continuous_cfcₙHomSuperset_left · cited by 1continuous_cfcₙHomSuperse…StarAlgHom.ext_adjoin · cited by 1StarAlgHom.ext_adjoingelfandTransform_bijective · cited by 1gelfandTransform_bijectiveDFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeStar.star · cited by 1082Star.starStar · cited by 496StarStarHomClass · cited by 76StarHomClassStarHomClass.map_starCITED BYCITES

Cites5

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

Cited by24

Results whose statement or proof uses this declaration.