Theorems · Theorem · commutative algebra

Module.DirectLimit.hom_ext_iff

∀ {R : Type u_1} [inst : Semiring R] {ι : Type u_2} [inst_1 : Preorder ι] {G : ι → Type u_3}
  [inst_2 : (i : ι) → AddCommMonoid (G i)] [inst_3 : (i : ι) → Module R (G i)] {f : (i j : ι) → i ≤ j → G i →ₗ[R] G j}
  [inst_4 : DecidableEq ι] {P : Type u_4} [inst_5 : AddCommMonoid P] [inst_6 : Module R P]
  {g₁ g₂ : Module.DirectLimit G f →ₗ[R] P},
  g₁ = g₂ ↔ ∀ (i : ι), g₁ ∘ₗ Module.DirectLimit.of R ι G f i = g₂ ∘ₗ Module.DirectLimit.of R ι G f i

Defined in

Mathlib.Algebra.Colimit.Module

Cited by

0 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPreorderAddCommMonoidModuleDecidableEqAddCommMonoidModule