Theorems · Definition · category theory
CategoryTheory.Under.mk
{T : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} T] → {X Y : T} → (X ⟶ Y) → CategoryTheory.Under XTo give an object in the under category, it suffices to give an arrow with domain X.
- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 25 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.
Cites4
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.Understatement · cited by 276
- CategoryTheory.StructuredArrow.mkproof · cited by 125
Cited by90
Results whose statement or proof uses this declaration.
- CategoryTheory.Under.postproof · cited by 24
- CommRingCat.mkUnderproof · cited by 24
- CategoryTheory.Under.pushoutproof · cited by 21
- CategoryTheory.Over.opEquivOpUnderproof · cited by 9
- CategoryTheory.Under.liftproof · cited by 9
- CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctorproof · cited by 8
- CategoryTheory.Under.opEquivOpOverproof · cited by 7
- CategoryTheory.Limits.pushoutCoconeEquivBinaryCofanstatement and proof · cited by 7
- CategoryTheory.Under.equivalenceOfIsInitialproof · cited by 7
- CategoryTheory.MorphismProperty.isFinitelyPresentableproof · cited by 6
- CategoryTheory.algebraToUnderproof · cited by 5
- CategoryTheory.Limits.Cone.toUnderproof · cited by 4