Theorems · Theorem · group theory
Submonoid.IsLocalizationMap.surj
∀ {M : Type u_1} [inst : CommMonoid M] {N : Type u_2} [inst_1 : CommMonoid N] {S : Submonoid M} {f : M → N},
S.IsLocalizationMap f → ∀ (z : N), ∃ x, z * f ↑x.2 = f x.1- Cited by
- 8 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CommMonoidCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- Submonoid.IsLocalizationMapstatement and proof · cited by 19
Cited by8
Results whose statement or proof uses this declaration.
- IsLocalization.surjproof · cited by 29
- Submonoid.LocalizationMap.surjproof · cited by 15
- AlgebraicGeometry.exists_eq_pow_mul_of_isAffineOpenproof · cited by 1
- Submonoid.isLocalizationMap_iff_bijectiveproof · cited by 1
- Algebra.essFiniteType_cond_iffproof · cited by 0
- Submonoid.IsLocalizationMap.mulEquiv_compproof · cited by 0
- Submonoid.IsLocalizationMap.piproof · cited by 0
- Submonoid.IsLocalizationMap.surj_pi_of_finiteproof · cited by 0