Theorems · Definition · category theory
CategoryTheory.Arrow.Hom.left
{T : Type u} → [inst : CategoryTheory.Category.{v, u} T] → {X Y : CategoryTheory.Arrow T} → (X ⟶ Y) → (X.left ⟶ Y.left)The left part of a morphism in the category of arrows.
- Defined in
- Mathlib.CategoryTheory.Comma.Arrow
- Cited by
- 160 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 51 definitions · uses no axioms
- 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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Arrowstatement and proof · cited by 713
- CategoryTheory.CommaMorphism.leftproof · cited by 526
- CategoryTheory.Arrow.leftstatement · cited by 426
Cited by206
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.mapArrowproof · cited by 31
- CategoryTheory.Arrow.hom_extstatement and proof · cited by 21
- CategoryTheory.Arrow.Hom.wstatement · cited by 17
- CategoryTheory.Square.fromArrowArrowFunctorproof · cited by 14
- CategoryTheory.Square.fromArrowArrowFunctor'proof · cited by 14
- CategoryTheory.Arrow.w_mk_rightstatement · cited by 13
- CategoryTheory.SmallObject.ιObjproof · cited by 11
- CategoryTheory.ParametrizedAdjunction.arrowHomEquivproof · cited by 11
- CategoryTheory.Functor.PushoutObjObj.mapArrowRightproof · cited by 11
- CategoryTheory.SmallObject.objMapproof · cited by 10
- CategoryTheory.Functor.PushoutObjObj.mapArrowLeftproof · cited by 10
- CategoryTheory.Limits.kernelSubobjectMapproof · cited by 9
Showing the 200 most cited of 206.