Theorems · Theorem · category theory
CategoryTheory.SmallObject.llp_rlp_of_isCardinalForSmallObjectArgument_aleph0
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (I : CategoryTheory.MorphismProperty C)
[I.IsCardinalForSmallObjectArgument Cardinal.aleph0],
I.rlp.llp =
((CategoryTheory.MorphismProperty.coproducts.{w, v, u} I).pushouts.transfiniteCompositionsOfShape ℕ).retracts- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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.MorphismPropertystatement and proof · cited by 2,179
- OrderIsoproof · cited by 874
- Cardinal.aleph0statement and proof · cited by 521
- OrderIso.symmproof · cited by 475
- Nonempty.someproof · cited by 340
- Cardinal.ordproof · cited by 266
- Ordinal.omega0proof · cited by 197
- Ordinal.ToTypeproof · cited by 143
- Ordinal.liftproof · cited by 86
- CategoryTheory.MorphismProperty.rlpstatement · cited by 53
- CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgumentstatement and proof · cited by 49
Cited by2
Results whose statement or proof uses this declaration.
- SSet.innerAnodyneExtensions_eq_retracts_transfiniteCompositionsOfShapeproof · cited by 0
- SSet.anodyneExtensions_eq_retracts_transfiniteCompositionsOfShapeproof · cited by 0