Theorems · Theorem · group theory

DirectSum.addHom_ext

∀ {ι : Type v} {β : ι → Type w} [inst : (i : ι) → AddCommMonoid (β i)] [inst_1 : DecidableEq ι] {γ : Type u_1}
  [inst_2 : AddZeroClass γ] ⦃f g : (DirectSum ι fun i => β i) →+ γ⦄,
  (∀ (i : ι) (y : β i), f ((DirectSum.of β i) y) = g ((DirectSum.of β i) y)) → f = g

If two additive homomorphisms from ⨁ i, β i are equal on each of β i y, then they are equal.

Defined in

Mathlib.Algebra.DirectSum.Basic

Cited by

1 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidDecidableEqAddZeroClass