Theorems · Theorem · general topology

ContinuousMap.compStarAlgHom_comp

∀ (X : Type u_1) {𝕜 : Type u_2} {A : Type u_3} {B : Type u_4} {C : Type u_5} [inst : TopologicalSpace X]
  [inst_1 : CommSemiring 𝕜] [inst_2 : TopologicalSpace A] [inst_3 : Semiring A] [inst_4 : IsTopologicalSemiring A]
  [inst_5 : Star A] [inst_6 : ContinuousStar A] [inst_7 : Algebra 𝕜 A] [inst_8 : TopologicalSpace B]
  [inst_9 : Semiring B] [inst_10 : IsTopologicalSemiring B] [inst_11 : Star B] [inst_12 : ContinuousStar B]
  [inst_13 : Algebra 𝕜 B] [inst_14 : TopologicalSpace C] [inst_15 : Semiring C] [inst_16 : IsTopologicalSemiring C]
  [inst_17 : Star C] [inst_18 : ContinuousStar C] [inst_19 : Algebra 𝕜 C] (φ : A →⋆ₐ[𝕜] B) (ψ : B →⋆ₐ[𝕜] C)
  (hφ : Continuous ⇑φ) (hψ : Continuous ⇑ψ),
  ContinuousMap.compStarAlgHom X (ψ.comp φ) ⋯ =
    (ContinuousMap.compStarAlgHom X ψ hψ).comp (ContinuousMap.compStarAlgHom X φ hφ)

ContinuousMap.compStarAlgHom is functorial.

Defined in

Mathlib.Topology.ContinuousMap.Star

Cited by

0 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCommSemiringTopologicalSpaceSemiringIsTopologicalSemiringStarContinuousStarAlgebraTopologicalSpaceSemiringIsTopologicalSemiringStarContinuousStarAlgebraTopologicalSpaceSemiringIsTopologicalSemiringStarContinuousStarAlgebra