Theorems · Theorem · category theory
CategoryTheory.SmallObject.isSmall
∀ {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.MorphismProperty.IsSmall.{w, v, u} I- Cited by
- 2 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
- Ordinal.ToTypestatement and proof · cited by 143
- CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgumentstatement and proof · cited by 49
- CategoryTheory.MorphismProperty.IsSmallstatement · cited by 9
- CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.isSmallproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.SmallObject.hasColimitsOfShape_discreteproof · cited by 7
- CategoryTheory.SmallObject.succStruct_prop_le_propArrowproof · cited by 0