Theorems · Theorem · commutative algebra

AddCommGroup.DirectLimit.lift_injective

∀ {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]
  (g : (i : ι) → G i →+ P) (Hg : ∀ (i j : ι) (hij : i ≤ j) (x : G i), (g j) ((f i j hij) x) = (g i) x)
  [IsDirectedOrder ι],
  (∀ (i : ι), Function.Injective ⇑(g i)) → Function.Injective ⇑(AddCommGroup.DirectLimit.lift G f P g Hg)

Defined in

Mathlib.Algebra.Colimit.Module

Cited by

0 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderAddCommMonoidDecidableEqAddCommMonoidIsDirectedOrder