Theorems · Theorem · commutative algebra

Module.Presentation.cokernel_var

∀ {A : Type u} [inst : Ring A] {M₁ : Type v₁} {M₂ : Type v₂} [inst_1 : AddCommGroup M₁] [inst_2 : Module A M₁]
  [inst_3 : AddCommGroup M₂] [inst_4 : Module A M₂] (pres₂ : Module.Presentation A M₂) {f : M₁ →ₗ[A] M₂} {ι : Type w₁}
  {g₁ : ι → M₁} (data : pres₂.CokernelData f g₁) (hg₁ : Submodule.span A (Set.range g₁) = ⊤)
  (g : (pres₂.cokernelRelations data).G), (pres₂.cokernel data hg₁).var g = Submodule.Quotient.mk (pres₂.var g)

Defined in

Mathlib.Algebra.Module.Presentation.Cokernel

Cited by

0 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddCommGroupModule