Theorems · Theorem · category theory

CategoryTheory.preservesColimitsOfShape_of_isCardinalPresentable

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (X : C) (κ : Cardinal.{w}) [inst_1 : Fact κ.IsRegular]
  [CategoryTheory.IsCardinalPresentable X κ] (J : Type w) [inst_3 : CategoryTheory.SmallCategory J]
  [CategoryTheory.IsCardinalFiltered J κ],
  CategoryTheory.Limits.PreservesColimitsOfShape J (CategoryTheory.coyoneda.obj (Opposite.op X))

Defined in: Mathlib.CategoryTheory.Presentable.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category Fact CategoryTheory.IsCardinalPresentable CategoryTheory.SmallCategory CategoryTheory.IsCardinalFiltered

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Cites13

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
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement · cited by 16,252
Oppositestatement · cited by 8,081
Factstatement and proof · cited by 2,726
Cardinalstatement and proof · cited by 2,598
CategoryTheory.SmallCategorystatement and proof · cited by 480
Cardinal.IsRegularstatement and proof · cited by 282
CategoryTheory.Limits.PreservesColimitsOfShapestatement · cited by 222
CategoryTheory.coyonedastatement and proof · cited by 208
CategoryTheory.IsCardinalFilteredstatement and proof · cited by 69
CategoryTheory.IsCardinalPresentablestatement and proof · cited by 39

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.isCardinalPresentable_of_equivalenceproof · cited by 0
CategoryTheory.Types.isCardinalPresentable_iffproof · cited by 0