Theorems · Theorem · group theory

DirectSum.decompose_lhom_ext

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [inst : DecidableEq ι] [inst_1 : Semiring R] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] (ℳ : ι → Submodule R M) [DirectSum.Decomposition ℳ] {N : Type u_5} [inst : AddCommMonoid N]
  [inst_4 : Module R N] ⦃f g : M →ₗ[R] N⦄, (∀ (i : ι), f ∘ₗ (ℳ i).subtype = g ∘ₗ (ℳ i).subtype) → f = g

Two linear maps from a module with a decomposition agree if they agree on every piece. Note this cannot be @[ext] as ℳ cannot be inferred.

Defined in

Mathlib.Algebra.DirectSum.Decomposition

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqSemiringAddCommMonoidModuleDirectSum.DecompositionAddCommMonoidModule