Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.ind_ind
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.ObjectProperty C},
P ≤ CategoryTheory.ObjectProperty.isFinitelyPresentable C →
∀ [CategoryTheory.LocallySmall.{w, v, u} C], P.ind.ind = P.indind is idempotent if P implies finitely presentable.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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.Functor.objproof · cited by 19,642
- le_antisymmproof · cited by 2,068
- CategoryTheory.Equivalence.inverseproof · cited by 1,130
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.SmallCategoryproof · cited by 480
- CategoryTheory.LocallySmallstatement and proof · cited by 242
- CategoryTheory.IsFilteredproof · cited by 210
- CategoryTheory.Limits.ColimitPresentation.diagproof · cited by 62
- CategoryTheory.Limits.ColimitPresentationproof · cited by 54
- CategoryTheory.ShrinkHomsproof · cited by 34
- CategoryTheory.ShrinkHoms.equivalenceproof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.ind_indproof · cited by 0