Theorems · Theorem · commutative algebra
IsLocalizedModule.iso_symm_comp
∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M : Type u_2} {M' : Type u_3} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid M'] [inst_3 : Module R M] [inst_4 : Module R M'] (f : M →ₗ[R] M')
[inst_5 : IsLocalizedModule S f], ↑(IsLocalizedModule.iso S f).symm ∘ₗ f = LocalizedModule.mkLinearMap S M- Cited by
- 5 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- Submonoidstatement and proof · cited by 3,086
- LinearMap.compstatement · cited by 1,642
- LinearEquiv.symmstatement and proof · cited by 1,461
- one_smulproof · cited by 1,374
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
- LinearMap.extproof · cited by 844
Cited by5
Results whose statement or proof uses this declaration.
- IsLocalizedModule.lift_compproof · cited by 4
- IsLocalizedModule.iso_symm_applyproof · cited by 3
- LocalizedModule.restrictScalars_map_eqproof · cited by 2
- IsLocalizedModule.iso_localizedModule_eq_reflproof · cited by 2
- Module.FinitePresentation.exists_basis_localizedModule_powersproof · cited by 1