Theorems · Theorem · ring theory

NonUnitalStarAlgHom.mk.injEq

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : Monoid R] [inst_1 : NonUnitalNonAssocSemiring A]
  [inst_2 : DistribMulAction R A] [inst_3 : Star A] [inst_4 : NonUnitalNonAssocSemiring B]
  [inst_5 : DistribMulAction R B] [inst_6 : Star B] (toNonUnitalAlgHom : A →ₙₐ[R] B)
  (map_star' : ∀ (a : A), toNonUnitalAlgHom.toFun (star a) = star (toNonUnitalAlgHom.toFun a))
  (toNonUnitalAlgHom_1 : A →ₙₐ[R] B)
  (map_star'_1 : ∀ (a : A), toNonUnitalAlgHom_1.toFun (star a) = star (toNonUnitalAlgHom_1.toFun a)),
  ({ toNonUnitalAlgHom := toNonUnitalAlgHom, map_star' := map_star' } =
      { toNonUnitalAlgHom := toNonUnitalAlgHom_1, map_star' := map_star'_1 }) =
    (toNonUnitalAlgHom = toNonUnitalAlgHom_1)

Defined in

Mathlib.Algebra.Star.StarAlgHom

Cited by

0 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext

Assumes

MonoidNonUnitalNonAssocSemiringDistribMulActionStarNonUnitalNonAssocSemiringDistribMulActionStar