Theorems · Definition · category theory
CategoryTheory.Over
{T : Type u₁} → [CategoryTheory.Category.{v₁, u₁} T] → T → Type (max u₁ v₁)The over category has as objects arrows in T with codomain X and as morphisms commutative
triangles.
- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 935 results in Mathlib
- Foundations
- Depth 24 from the axioms, rests on 122 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.CostructuredArrowproof · cited by 536
Cited by1,338
Results whose statement or proof uses this declaration.
- CategoryTheory.Over.leftstatement and proof · cited by 541
- CategoryTheory.Over.homstatement and proof · cited by 370
- CategoryTheory.Over.Hom.leftstatement and proof · cited by 287
- CategoryTheory.Over.mkstatement · cited by 203
- CategoryTheory.Over.forgetstatement · cited by 164
- CategoryTheory.GrothendieckTopology.overstatement and proof · cited by 115
- CategoryTheory.Over.homMkstatement and proof · cited by 115
- CategoryTheory.Over.isMonostatement and proof · cited by 111
- CategoryTheory.Over.mapstatement · cited by 97
- CategoryTheory.Over.cartesianMonoidalCategorystatement and proof · cited by 68
- CategoryTheory.ChosenPullbacksAlong.pullbackstatement · cited by 62
- CategoryTheory.Over.pullbackstatement and proof · cited by 53
Showing the 200 most cited of 1,338.