Theorems · Definition · category theory
CategoryTheory.Prod.swap
(C : Type u₁) →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
(D : Type u₂) → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor (C × D) (D × C)The functor swapping the factors of a Cartesian product of categories, C × D ⥤ D × C.
- Defined in
- Mathlib.CategoryTheory.Products.Basic
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Prod.mkHomproof · cited by 108
Cited by47
Results whose statement or proof uses this declaration.
- CategoryTheory.Prod.braidingproof · cited by 24
- CategoryTheory.Functor.uncurryObjFlipstatement · cited by 8
- CategoryTheory.Functor.flipIsoCurrySwapUncurrystatement · cited by 6
- CategoryTheory.Limits.colimitLimitToLimitColimitstatement and proof · cited by 6
- CategoryTheory.Limits.ι_colimitLimitToLimitColimit_πstatement and proof · cited by 3
- CategoryTheory.Limits.limitIsoSwapCompLimstatement · cited by 3
- CategoryTheory.Prod.symmetrystatement · cited by 2
- CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColimstatement and proof · cited by 2
- CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLimstatement and proof · cited by 2
- CategoryTheory.Limits.colimitIsoSwapCompColimstatement · cited by 2
- CategoryTheory.MonoidalCategory.externalProductSwapstatement and proof · cited by 2
- CategoryTheory.MonoidalOpposite.tensorIsostatement · cited by 2