Theorems · Definition · category theory
CategoryTheory.Under.Hom.right
{T : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} T] → {X : T} → {f g : CategoryTheory.Under X} → (f ⟶ g) → (f.right ⟶ g.right)The morphism that is part of a morphism in Under X.
- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 67 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, 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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CommaMorphism.rightproof · cited by 391
- CategoryTheory.Understatement and proof · cited by 276
- CategoryTheory.Under.rightstatement · cited by 128
Cited by81
Results whose statement or proof uses this declaration.
- CategoryTheory.Under.postproof · cited by 24
- CategoryTheory.Under.pushoutproof · cited by 21
- CommRingCat.toAlgHomproof · cited by 13
- CategoryTheory.Under.wstatement · cited by 10
- CategoryTheory.Over.opEquivOpUnderproof · cited by 9
- CategoryTheory.Under.UnderMorphism.extstatement and proof · cited by 8
- CategoryTheory.Under.opEquivOpOverproof · cited by 7
- CategoryTheory.Limits.pushoutCoconeEquivBinaryCofanproof · cited by 7
- CategoryTheory.underToAlgebraproof · cited by 6
- CategoryTheory.Under.mapPushoutAdjproof · cited by 4
- CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit_underproof · cited by 2
- CommRingCat.Under.equalizerForkIsLimitproof · cited by 2