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Theorems · Theorem · commutative algebra

AddCommGroup.DirectLimit.hom_ext_iff

∀ {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},
  g₁ = g₂ ↔ ∀ (i : ι), g₁.comp (AddCommGroup.DirectLimit.of G f i) = g₂.comp (AddCommGroup.DirectLimit.of 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
PreorderAddCommMonoidDecidableEqAddCommMonoid
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AddCommMonoid · cited by 12281AddCommMonoidPreorder · cited by 7952PreorderAddMonoidHom · cited by 3230AddMonoidHomAddMonoidHom.comp · cited by 339AddMonoidHom.compAddCommGroup.DirectLimit · cited by 16AddCommGroup.DirectLimitAddCommGroup.DirectLimit.of · cited by 13DirectLimit.ofAddCommGroup.DirectLimit.hom_ext · cited by 5DirectLimit.hom_extDirectLimit.hom_ext_iffCITED BYCITES

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