Theorems · Theorem · category theory

CategoryTheory.Limits.Bicones.functoriality_map_hom

∀ {J : Type w} {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] (F : J → C) (G : CategoryTheory.Functor C D)
  [inst_4 : G.PreservesZeroMorphisms] {X Y : CategoryTheory.Limits.Bicone F} (f : X ⟶ Y),
  ((CategoryTheory.Limits.Bicones.functoriality F G).map f).hom = G.map f.hom

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Biproducts

Cited by

0 results in Mathlib

Foundations

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

Assumes

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