Theorems · Definition · category theory

CategoryTheory.Limits.PreservesBiproduct.casesOn

{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] →
            {J : Type w₁} →
              {f : J → C} →
                {F : CategoryTheory.Functor C D} →
                  [inst_4 : F.PreservesZeroMorphisms] →
                    {motive : CategoryTheory.Limits.PreservesBiproduct f F → Sort u} →
                      (t : CategoryTheory.Limits.PreservesBiproduct f F) →
                        ((preserves :
                              ∀ {b : CategoryTheory.Limits.Bicone f} (a : b.IsBilimit),
                                Nonempty (F.mapBicone b).IsBilimit) →
                            motive ⋯) →
                          motive t

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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