Theorems · Definition · category theory
CategoryTheory.Prod.braiding
(C : Type u₁) →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
(D : Type u₂) → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → C × D ≌ D × CThe equivalence, given by swapping factors, between C × D and D × C.
- Defined in
- Mathlib.CategoryTheory.Products.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.compproof · cited by 6,529
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Prod.swapproof · cited by 36
Cited by30
Results whose statement or proof uses this declaration.
- CategoryTheory.prod.prodμproof · cited by 8
- CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIsostatement · cited by 4
- CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColimproof · cited by 4
- CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLimproof · cited by 4
- CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColimproof · cited by 2
- CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLimproof · cited by 2
- CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_homproof · cited by 1
- CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_invproof · cited by 1
- CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_πproof · cited by 1
- CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_πproof · cited by 1
- CategoryTheory.prod.prodμ_counitIso_hom_appstatement · cited by 0
- CategoryTheory.prod.prodμ_counitIso_inv_appstatement · cited by 0