Theorems · Definition · category theory
CategoryTheory.Arrow.leftFunc
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Functor (CategoryTheory.Arrow C) CThe functor sending an arrow to its source.
- Defined in
- Mathlib.CategoryTheory.Comma.Arrow
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Functorstatement · cited by 16,252
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.Arrowstatement · cited by 713
- CategoryTheory.Comma.fstproof · cited by 76
Cited by61
Results whose statement or proof uses this declaration.
- TopPair.proj₂proof · cited by 15
- CategoryTheory.Arrow.leftToRightstatement · cited by 10
- HomotopicalAlgebra.AttachCells.ofArrowIsoproof · cited by 9
- CategoryTheory.MorphismProperty.FunctorialFactorizationData.istatement · cited by 7
- CategoryTheory.Arrow.leftFunc_mapstatement and proof · cited by 5
- CategoryTheory.TransfiniteCompositionOfShape.ofArrowIsoproof · cited by 4
- CategoryTheory.SmallObject.relativeCellComplexιObjproof · cited by 4
- CategoryTheory.Limits.ker.ιstatement · cited by 3
- CategoryTheory.SmallObject.relativeCellComplexιObjFObjSuccIsoproof · cited by 3
- CategoryTheory.RetractArrow.leftproof · cited by 3
- CategoryTheory.MorphismProperty.FunctorialFactorizationData.facstatement · cited by 2
- CategoryTheory.ObjectProperty.SerreClassLocalization.hasCokernelsproof · cited by 1