Theorems · Theorem · commutative algebra

AddCommGroup.DirectLimit.hom_ext

∀ {ι : Type u_2} [inst : Preorder ι] {G : ι → Type u_3} [inst_1 : (i : ι) → AddCommMonoid (G i)]
  {f : (i j : ι) → i ≤ j → G i →+ G j} [inst_2 : DecidableEq ι] (P : Type u_4) [inst_3 : AddCommMonoid P]
  {g₁ g₂ : AddCommGroup.DirectLimit G f →+ P},
  (∀ (i : ι), g₁.comp (AddCommGroup.DirectLimit.of G f i) = g₂.comp (AddCommGroup.DirectLimit.of G f i)) → g₁ = g₂

Defined in

Mathlib.Algebra.Colimit.Module

Cited by

5 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderAddCommMonoidDecidableEqAddCommMonoid