Theorems · Theorem · commutative algebra
RingHom.surjective_iff_epi_and_finite
∀ {R S : CommRingCat} {f : R ⟶ S},
Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f) ↔ CategoryTheory.Epi f ∧ (CommRingCat.Hom.hom f).Finite- Defined in
- Mathlib.Algebra.Category.Ring.Epi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- RingHomstatement · cited by 10,189
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement · cited by 1,096
- CategoryTheory.Epistatement and proof · cited by 688
- CommRingCat.Hom.homstatement and proof · cited by 432
- RingHom.Finitestatement and proof · cited by 48
- CategoryTheory.ConcreteCategory.epi_of_surjectiveproof · cited by 9
- RingHom.Finite.of_surjectiveproof · cited by 8
- RingHom.surjective_of_epi_of_finiteproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsClosedImmersion.iff_isFinite_and_monoproof · cited by 2