Theorems · Definition · category theory

CategoryTheory.Limits.BinaryBicones.functoriality

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {D : Type uD} →
        [inst_2 : CategoryTheory.Category.{uD', uD} D] →
          [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] →
            (P Q : C) →
              (F : CategoryTheory.Functor C D) →
                [F.PreservesZeroMorphisms] →
                  CategoryTheory.Functor (CategoryTheory.Limits.BinaryBicone P Q)
                    (CategoryTheory.Limits.BinaryBicone (F.obj P) (F.obj Q))

A functor F : C ⥤ D sends binary bicones for P and Q to binary bicones for G.obj P and G.obj Q functorially.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts

Cited by

7 results in Mathlib

Foundations

Depth 15 from the axioms · uses propext, Quot.sound

Assumes

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