Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.braiding_hom

∀ {C : Type uC} [inst : CategoryTheory.Category.{uC', uC} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] (P Q : C),
  (CategoryTheory.Limits.biprod.braiding P Q).hom =
    CategoryTheory.Limits.biprod.lift CategoryTheory.Limits.biprod.snd CategoryTheory.Limits.biprod.fst
Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
4 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproducts
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Limits.biprod.braid_natural · cited by 1biprod.braid_naturalCategoryTheory.Limits.biprod.braiding_map_braiding · cited by 1biprod.braiding_map_braid…CategoryTheory.Limits.biprod.symmetry · cited by 1biprod.symmetryCategoryTheory.Limits.biprod.braiding'_eq_braiding · cited by 0biprod.braiding'_eq_braid…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.biprod · cited by 312Limits.biprodCategoryTheory.Limits.HasBinaryBiproducts · cited by 165Limits.HasBinaryBiproductsCategoryTheory.Limits.biprod.snd · cited by 132biprod.sndCategoryTheory.Limits.biprod.fst · cited by 121biprod.fstCategoryTheory.Limits.biprod.lift · cited by 79biprod.liftCategoryTheory.Limits.biprod.braiding · cited by 9biprod.braidingbiprod.braiding_homCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.