Theorems · Theorem · commutative algebra

IsLocalizedModule.lift_apply

∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {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 : M →ₗ[R] M') [inst_7 : IsLocalizedModule S f] (g : M →ₗ[R] M'')
  (h : ∀ (x : ↥S), IsUnit ((algebraMap R (Module.End R M'')) ↑x)) (x : M), (IsLocalizedModule.lift S f g h) (f x) = g x

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

5 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleIsLocalizedModule