Theorems · Definition · category theory
CategoryTheory.MorphismProperty.homFamily
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(P : CategoryTheory.MorphismProperty C) → (f : ↑P.toSet) → (↑f).left ⟶ (↑f).rightThe family of morphisms indexed by P.toSet which corresponds
to P : MorphismProperty C, see MorphismProperty.ofHoms_homFamily.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Quiver.Homstatement · cited by 32,603
- Set.Elemstatement and proof · cited by 7,166
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Arrowstatement · cited by 713
- CategoryTheory.Arrow.leftstatement · cited by 426
- CategoryTheory.Arrow.rightstatement · cited by 423
- CategoryTheory.Arrow.homproof · cited by 335
- CategoryTheory.MorphismProperty.toSetstatement and proof · cited by 26
Cited by21
Results whose statement or proof uses this declaration.
- CategoryTheory.SmallObject.hasColimitsOfShape_discretestatement and proof · cited by 7
- CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIsostatement · cited by 5
- CategoryTheory.SmallObject.relativeCellComplexιObjstatement · cited by 4
- CategoryTheory.SmallObject.succStructproof · cited by 3
- CategoryTheory.SmallObject.relativeCellComplexιObjFObjSuccIsostatement · cited by 3
- CategoryTheory.MorphismProperty.ofHoms_homFamilystatement and proof · cited by 2
- CategoryTheory.SmallObject.transfiniteCompositionsOfShape_ιObjproof · cited by 2
- CategoryTheory.SmallObject.ιFunctorObj_eqstatement and proof · cited by 1
- CategoryTheory.SmallObject.hasRightLiftingProperty_πObjproof · cited by 1
- CategoryTheory.SmallObject.πFunctorObj_eqstatement and proof · cited by 1
- CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_compstatement and proof · cited by 1
- CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assocstatement · cited by 1