Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.le_isCardinalPresentable
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.ObjectProperty C} {κ : Cardinal.{w}}
[inst_1 : Fact κ.IsRegular], P.IsCardinalFilteredGenerator κ → P ≤ CategoryTheory.isCardinalPresentable C κ- Cited by
- 8 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.CategoryFact
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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Factstatement and proof · cited by 2,726
- Cardinalstatement and proof · cited by 2,598
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- Cardinal.IsRegularstatement and proof · cited by 282
- CategoryTheory.ObjectProperty.IsCardinalFilteredGeneratorstatement and proof · cited by 22
- CategoryTheory.isCardinalPresentablestatement · cited by 20
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCardinalLocallyPresentable.iff_exists_isStrongGeneratorproof · cited by 1
- CategoryTheory.Adjunction.isCardinalFilteredGeneratorproof · cited by 1
- CategoryTheory.HasCardinalFilteredGenerator.exists_small_generatorproof · cited by 1
- CategoryTheory.isCardinalFilteredGenerator_isCardinalPresentableproof · cited by 1
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isoClosureproof · cited by 1
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isoClosure_iffproof · cited by 1
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.presentableproof · cited by 0