Theorems · Definition · category theory
CategoryTheory.Arrow.hom
{T : Type u} → [inst : CategoryTheory.Category.{v, u} T] → (X : CategoryTheory.Arrow T) → X.left ⟶ X.rightGiven X : Arrow T, this is the morphism X.left ⟶ X.right.
- Defined in
- Mathlib.CategoryTheory.Comma.Arrow
- Cited by
- 335 results in Mathlib
- Foundations
- Depth 13 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.
Cites6
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 · cited by 32,603
- CategoryTheory.Arrowstatement and proof · cited by 713
- CategoryTheory.Comma.homproof · cited by 490
- CategoryTheory.Arrow.leftstatement · cited by 426
- CategoryTheory.Arrow.rightstatement · cited by 423
Cited by452
Results whose statement or proof uses this declaration.
- CategoryTheory.Arrow.isoMkstatement and proof · cited by 53
- CategoryTheory.Arrow.homMkstatement and proof · cited by 35
- CategoryTheory.Functor.mapArrowproof · cited by 31
- CategoryTheory.MorphismProperty.toSetproof · cited by 26
- CategoryTheory.Limits.multicospanIndexEndproof · cited by 22
- CategoryTheory.Arrow.cechNervestatement and proof · cited by 18
- CategoryTheory.Arrow.Hom.wstatement · cited by 17
- CategoryTheory.Limits.HasImageMapstatement · cited by 17
- CategoryTheory.Limits.multispanIndexCoendproof · cited by 17
- CategoryTheory.Limits.ImageMapstatement · cited by 17
- CategoryTheory.Arrow.augmentedCechNervestatement and proof · cited by 16
- CategoryTheory.MorphismProperty.homFamilyproof · cited by 14
Showing the 200 most cited of 452.