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Theorems · Theorem · category theory

CategoryTheory.SmallObject.hasCoproducts

∀ {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.HasCoproducts C
Defined in
Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument
Cited by
1 results in Mathlib
Foundations
Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryFactOrderBotCategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument
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Around this declaration

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

CategoryTheory.SmallObject.hasColimitsOfShape_discrete · cited by 7SmallObject.hasColimitsOf…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.ordOrdinal.ToType · cited by 143Ordinal.ToTypeCategoryTheory.Limits.HasCoproducts · cited by 119Limits.HasCoproductsCategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument · cited by 49MorphismProperty.IsCardin…CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.hasCoproducts · cited by 1IsCardinalForSmallObjectA…SmallObject.hasCoproductsCITED BYCITES

Cites11

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Cited by1

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