Theorems · Theorem · category theory
CommRingCat.essentiallySmall_of_finiteType
∀ {P Q : CategoryTheory.ObjectProperty CommRingCat} [CategoryTheory.ObjectProperty.EssentiallySmall.{u, u, u + 1} Q],
(∀ (S : CommRingCat), P S → ∃ R, Q R ∧ ∃ f, (CommRingCat.Hom.hom f).FiniteType) →
CategoryTheory.ObjectProperty.EssentiallySmall.{u, u, u + 1} P- Defined in
- Mathlib.Algebra.Category.Ring.Small
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.invproof · cited by 6,514
- Algebra.algebraMapproof · cited by 4,706
- CategoryTheory.Isoproof · cited by 3,963
- CommRingCatstatement and proof · cited by 2,333
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- RingEquivproof · cited by 1,147
- CommRingCat.carrierstatement and proof · cited by 1,096
- CategoryTheory.Iso.symmproof · cited by 993
- RingHom.compproof · cited by 899
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.essentiallySmall_costructuredArrow_Specproof · cited by 0