Theorems · Theorem · ring theory

LinearMap.comp_apply

∀ {R₁ : Type u_2} {R₂ : Type u_3} {R₃ : Type u_4} {M₁ : Type u_9} {M₂ : Type u_10} {M₃ : Type u_11} [inst : Semiring R₁]
  [inst_1 : Semiring R₂] [inst_2 : Semiring R₃] [inst_3 : AddCommMonoid M₁] [inst_4 : AddCommMonoid M₂]
  [inst_5 : AddCommMonoid M₃] {module_M₁ : Module R₁ M₁} {module_M₂ : Module R₂ M₂} {module_M₃ : Module R₃ M₃}
  {σ₁₂ : R₁ →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R₁ →+* R₃} [inst_6 : RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] (f : M₂ →ₛₗ[σ₂₃] M₃)
  (g : M₁ →ₛₗ[σ₁₂] M₂) (x : M₁), (f ∘ₛₗ g) x = f (g x)

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

76 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringSemiringAddCommMonoidAddCommMonoidAddCommMonoidRingHomCompTriple