Theorems · Definition · category theory
CategoryTheory.Arrow
(T : Type u) → [CategoryTheory.Category.{v, u} T] → Type (max u v)The arrow category of T has as objects all morphisms in T and as morphisms commutative
squares in T.
- Defined in
- Mathlib.CategoryTheory.Comma.Arrow
- Cited by
- 713 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 44 definitions · uses no axioms
- 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.Commaproof · cited by 566
Cited by994
Results whose statement or proof uses this declaration.
- CategoryTheory.Arrow.leftstatement and proof · cited by 426
- CategoryTheory.Arrow.rightstatement and proof · cited by 423
- CategoryTheory.Arrow.mkstatement · cited by 421
- CategoryTheory.Arrow.homstatement and proof · cited by 335
- CategoryTheory.Arrow.Hom.rightstatement and proof · cited by 176
- CategoryTheory.Arrow.Hom.leftstatement and proof · cited by 160
- CategoryTheory.MorphismProperty.arrow_mk_iso_iffstatement · cited by 78
- CategoryTheory.MonoidalCategory.Arrow.pushoutProductstatement · cited by 64
- CategoryTheory.Arrow.isoMkstatement and proof · cited by 53
- CategoryTheory.Arrow.leftFuncstatement · cited by 37
- CategoryTheory.Arrow.homMkstatement and proof · cited by 35
- CategoryTheory.Arrow.rightFuncstatement · cited by 32
Showing the 200 most cited of 994.