Theorems · Definition · category theory
CategoryTheory.Under.hom
{T : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} T] → {X : T} → (f : CategoryTheory.Under X) → X ⟶ f.rightThe morphism that is part of an object in Under X.
- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 73 results in Mathlib
- Foundations
- Depth 26 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 · cited by 32,603
- CategoryTheory.Comma.homproof · cited by 490
- CategoryTheory.Understatement and proof · cited by 276
- CategoryTheory.Under.rightstatement · cited by 128
Cited by93
Results whose statement or proof uses this declaration.
- CategoryTheory.Under.homMkstatement and proof · cited by 43
- CategoryTheory.Under.postproof · cited by 24
- CategoryTheory.Under.pushoutproof · cited by 21
- CategoryTheory.Under.isoMkstatement and proof · cited by 11
- CategoryTheory.MorphismProperty.underObjproof · cited by 10
- CategoryTheory.Under.wstatement · cited by 10
- CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverseproof · cited by 10
- CategoryTheory.Over.opEquivOpUnderproof · cited by 9
- CategoryTheory.Under.opEquivOpOverproof · cited by 7
- CategoryTheory.WithInitial.commaFromUnderproof · cited by 7
- CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.gproof · cited by 6
- CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverseproof · cited by 6