Theorems · Definition · category theory
CategoryTheory.Over.hom
{T : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} T] → {X : T} → (f : CategoryTheory.Over X) → f.left ⟶ XThe morphism that is part of an object in Over X.
- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 370 results in Mathlib
- Foundations
- Depth 26 from the axioms, rests on 127 definitions · 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.Overstatement and proof · cited by 935
- CategoryTheory.Over.leftstatement · cited by 541
- CategoryTheory.Comma.homproof · cited by 490
Cited by463
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.arrowproof · cited by 175
- CategoryTheory.Over.homMkstatement and proof · cited by 115
- CategoryTheory.Over.isMonoproof · cited by 111
- CategoryTheory.Over.cartesianMonoidalCategoryproof · cited by 68
- CategoryTheory.Over.pullbackproof · cited by 53
- CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryOverproof · cited by 49
- CategoryTheory.ChosenPullbacksAlong.sndproof · cited by 45
- CategoryTheory.Over.postproof · cited by 44
- CategoryTheory.Over.wstatement · cited by 42
- CategoryTheory.MonoOver.arrowproof · cited by 41
- CategoryTheory.Presieve.categoryproof · cited by 38
- CategoryTheory.Presieve.coconestatement and proof · cited by 23
Showing the 200 most cited of 463.