Theorems · Definition · category theory
CategoryTheory.MorphismProperty.toSet
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → Set (CategoryTheory.Arrow C)The set in Set (Arrow C) which corresponds to P : MorphismProperty C.
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Set.ofPredproof · cited by 6,101
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Arrowstatement and proof · cited by 713
- CategoryTheory.Arrow.leftproof · cited by 426
- CategoryTheory.Arrow.rightproof · cited by 423
- CategoryTheory.Arrow.homproof · cited by 335
Cited by38
Results whose statement or proof uses this declaration.
- CategoryTheory.OrthogonalReflection.D₁proof · cited by 35
- CategoryTheory.MorphismProperty.homFamilystatement and proof · cited by 14
- CategoryTheory.MorphismProperty.ofHoms_iffproof · cited by 8
- CategoryTheory.MorphismProperty.HasCardinalLTproof · cited by 8
- CategoryTheory.SmallObject.hasColimitsOfShape_discretestatement · cited by 7
- CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIsostatement · cited by 5
- CategoryTheory.SmallObject.relativeCellComplexιObjstatement · cited by 4
- CategoryTheory.MorphismProperty.arrow_mk_mem_toSet_iffstatement · cited by 4
- CategoryTheory.SmallObject.relativeCellComplexιObjFObjSuccIsostatement · cited by 3
- CategoryTheory.OrthogonalReflection.D₂proof · cited by 3
- CategoryTheory.MorphismProperty.ofHoms_homFamilystatement and proof · cited by 2
- CategoryTheory.SmallObject.SuccStruct.prop_iffproof · cited by 1