Theorems · Theorem · linear algebra

Submodule.map_comp

∀ {R : Type u_1} {R₂ : Type u_3} {R₃ : Type u_4} {M : Type u_5} {M₂ : Type u_7} {M₃ : Type u_8} [inst : Semiring R]
  [inst_1 : Semiring R₂] [inst_2 : Semiring R₃] [inst_3 : AddCommMonoid M] [inst_4 : AddCommMonoid M₂]
  [inst_5 : AddCommMonoid M₃] [inst_6 : Module R M] [inst_7 : Module R₂ M₂] [inst_8 : Module R₃ M₃] {σ₁₂ : R →+* R₂}
  {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃} [inst_9 : RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [inst_10 : RingHomSurjective σ₁₂]
  [inst_11 : RingHomSurjective σ₂₃] [inst_12 : RingHomSurjective σ₁₃] (f : M →ₛₗ[σ₁₂] M₂) (g : M₂ →ₛₗ[σ₂₃] M₃)
  (p : Submodule R M), Submodule.map (g ∘ₛₗ f) p = Submodule.map g (Submodule.map f p)

Defined in

Mathlib.Algebra.Module.Submodule.Map

Cited by

19 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleRingHomCompTripleRingHomSurjectiveRingHomSurjectiveRingHomSurjective