Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.exists_colimitsOfShape
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.ObjectProperty C} {κ : Cardinal.{w}}
[inst_1 : Fact κ.IsRegular],
P.IsCardinalFilteredGenerator κ →
∀ (X : C), ∃ J x, ∃ (_ : CategoryTheory.IsCardinalFiltered J κ), P.colimitsOfShape J X- Cited by
- 7 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses Quot.sound
- Assumes
- CategoryTheory.CategoryFact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CategoryTheory.SmallCategorystatement · cited by 480
- Cardinal.IsRegularstatement and proof · cited by 282
- CategoryTheory.IsCardinalFilteredstatement · cited by 69
- CategoryTheory.ObjectProperty.colimitsOfShapestatement · cited by 35
- CategoryTheory.ObjectProperty.IsCardinalFilteredGeneratorstatement and proof · cited by 22
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Adjunction.isCardinalFilteredGeneratorproof · cited by 1
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.presentableproof · cited by 0