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Theorems · Theorem · category theory

CategoryTheory.SmallObject.hasPushouts

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (I : CategoryTheory.MorphismProperty C) (κ : Cardinal.{w})
  [inst_1 : Fact κ.IsRegular] [inst_2 : OrderBot κ.ord.ToType] [I.IsCardinalForSmallObjectArgument κ],
  CategoryTheory.Limits.HasPushouts C
Defined in
Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument
Cited by
7 results in Mathlib
Foundations
Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryFactOrderBotCategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso · cited by 5SmallObject.iterationFunc…CategoryTheory.SmallObject.relativeCellComplexιObjFObjSuccIso · cited by 3SmallObject.relativeCellC…CategoryTheory.SmallObject.πFunctorObj_eq · cited by 1SmallObject.πFunctorObj_eqCategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp · cited by 1SmallObject.iterationFunc…CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc · cited by 1SmallObject.iterationFunc…CategoryTheory.SmallObject.ιFunctorObj_eq · cited by 1SmallObject.ιFunctorObj_eqCategoryTheory.SmallObject.hasRightLiftingProperty_πObj · cited by 1SmallObject.hasRightLifti…CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left · cited by 0SmallObject.iterationFunc…CategoryTheory.SmallObject.succStruct_prop_le_propArrow · cited by 0SmallObject.succStruct_pr…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryFact · cited by 2726FactCardinal · cited by 2598CardinalCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…OrderBot · cited by 1055OrderBotCardinal.IsRegular · cited by 282Cardinal.IsRegularCardinal.ord · cited by 266Cardinal.ordCategoryTheory.Limits.HasPushouts · cited by 172Limits.HasPushoutsOrdinal.ToType · cited by 143Ordinal.ToTypeCategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument · cited by 49MorphismProperty.IsCardin…CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.hasPushouts · cited by 1IsCardinalForSmallObjectA…SmallObject.hasPushoutsCITED BYCITES

Cites11

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Cited by9

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