Theorems · Theorem · commutative algebra

IsLocalizedModule.lift.congr_simp

∀ {R : Type u_1} [inst : CommSemiring R] (S S_1 : Submonoid R) (e_S : S = S_1) {M : Type u_2} {M' : Type u_3}
  {M'' : Type u_4} [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M'] [inst_3 : AddCommMonoid M'']
  [inst_4 : Module R M] [inst_5 : Module R M'] [inst_6 : Module R M''] (f f_1 : M →ₗ[R] M') (e_f : f = f_1)
  [inst_7 : IsLocalizedModule S f] (g g_1 : M →ₗ[R] M''),
  g = g_1 →
    ∀ (h : ∀ (x : ↥S), IsUnit ((algebraMap R (Module.End R M'')) ↑x)),
      IsLocalizedModule.lift S f g h = IsLocalizedModule.lift S_1 f_1 g_1 ⋯

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

0 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleIsLocalizedModule