Theorems · Definition · category theory

CategoryTheory.Limits.PreservesBinaryBiproduct.recOn

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
          [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] →
            {X Y : C} →
              {F : CategoryTheory.Functor C D} →
                [inst_4 : F.PreservesZeroMorphisms] →
                  {motive : CategoryTheory.Limits.PreservesBinaryBiproduct X Y F → Sort u} →
                    (t : CategoryTheory.Limits.PreservesBinaryBiproduct X Y F) →
                      ((preserves :
                            ∀ {b : CategoryTheory.Limits.BinaryBicone X Y} (a : b.IsBilimit),
                              Nonempty (F.mapBinaryBicone b).IsBilimit) →
                          motive ⋯) →
                        motive t

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphisms