Theorems · Theorem · commutative algebra
HomogeneousLocalization.mk_surjective
∀ {ι : Type u_1} {A : Type u_2} {σ : Type u_3} [inst : CommRing A] [inst_1 : SetLike σ A] {𝒜 : ι → σ} {x : Submonoid A},
Function.Surjective HomogeneousLocalization.mk- Cited by
- 14 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Submonoidstatement and proof · cited by 3,086
- SetLikestatement and proof · cited by 1,084
- HomogeneousLocalization.NumDenSameDegstatement · cited by 78
- HomogeneousLocalizationstatement · cited by 69
- HomogeneousLocalization.mkstatement · cited by 55
- Quotient.mk''_surjectiveproof · cited by 19
Cited by14
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eqproof · cited by 3
- AlgebraicGeometry.Proj.awayMap_awayToSectionproof · cited by 2
- HomogeneousLocalization.Away.mk_surjectiveproof · cited by 2
- HomogeneousLocalization.val_localRingHomproof · cited by 2
- HomogeneousLocalization.map_compproof · cited by 2
- AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpecproof · cited by 1
- HomogeneousLocalization.range_awayMapAux_subsetproof · cited by 1
- HomogeneousLocalization.Away.span_mk_prod_pow_eq_topproof · cited by 1
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_applyproof · cited by 1
- HomogeneousLocalization.isUnit_iff_isUnit_valproof · cited by 1
- HomogeneousLocalization.map_idproof · cited by 1
- AlgebraicGeometry.Proj.localRingHom_comp_stalkIsoproof · cited by 1