Theorems · Theorem · functional analysis

ContinuousLinearMap.neg_comp

∀ {R : Type u_1} [inst : Ring R] {R₂ : Type u_2} [inst_1 : Ring R₂] {R₃ : Type u_3} [inst_2 : Ring R₃] {M : Type u_4}
  [inst_3 : TopologicalSpace M] [inst_4 : AddCommGroup M] {M₂ : Type u_5} [inst_5 : TopologicalSpace M₂]
  [inst_6 : AddCommGroup M₂] {M₃ : Type u_6} [inst_7 : TopologicalSpace M₃] [inst_8 : AddCommGroup M₃]
  [inst_9 : Module R M] [inst_10 : Module R₂ M₂] [inst_11 : Module R₃ M₃] {σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃}
  {σ₁₃ : R →+* R₃} [inst_12 : RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [inst_13 : IsTopologicalAddGroup M₃] (g : M₂ →SL[σ₂₃] M₃)
  (f : M →SL[σ₁₂] M₂), (-g) ∘SL f = -g ∘SL f

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

2 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

RingRingRingTopologicalSpaceAddCommGroupTopologicalSpaceAddCommGroupTopologicalSpaceAddCommGroupModuleModuleModuleRingHomCompTripleIsTopologicalAddGroup