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- Cited by
- 7 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.MorphismPropertystatement and proof · cited by 2,179
- OrderBotstatement and proof · cited by 1,055
- Cardinal.IsRegularstatement and proof · cited by 282
- Cardinal.ordstatement and proof · cited by 266
- CategoryTheory.Limits.HasPushoutsstatement · cited by 172
- Ordinal.ToTypestatement and proof · cited by 143
- CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgumentstatement and proof · cited by 49
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIsostatement · cited by 5
- CategoryTheory.SmallObject.relativeCellComplexιObjFObjSuccIsostatement · cited by 3
- CategoryTheory.SmallObject.πFunctorObj_eqstatement · cited by 1
- CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_compstatement · cited by 1
- CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assocstatement · cited by 1
- CategoryTheory.SmallObject.ιFunctorObj_eqstatement · cited by 1
- CategoryTheory.SmallObject.hasRightLiftingProperty_πObjproof · cited by 1
- CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_leftstatement · cited by 0
- CategoryTheory.SmallObject.succStruct_prop_le_propArrowproof · cited by 0