Theorems · Theorem · category theory

CategoryTheory.NatTrans.mapHomotopyCategory_comp

∀ {ι : Type u_2} {V : Type u} [inst : CategoryTheory.Category.{v, u} V] [inst_1 : CategoryTheory.Preadditive V]
  {W : Type u_3} [inst_2 : CategoryTheory.Category.{v_1, u_3} W] [inst_3 : CategoryTheory.Preadditive W]
  (c : ComplexShape ι) {F G H : CategoryTheory.Functor V W} [inst_4 : F.Additive] [inst_5 : G.Additive]
  [inst_6 : H.Additive] (α : F ⟶ G) (β : G ⟶ H),
  CategoryTheory.NatTrans.mapHomotopyCategory (CategoryTheory.CategoryStruct.comp α β) c =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.NatTrans.mapHomotopyCategory α c)
      (CategoryTheory.NatTrans.mapHomotopyCategory β c)

Defined in: Mathlib.Algebra.Homology.HomotopyCategory
Cited by: 0 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Functor.Additive CategoryTheory.Functor.Additive CategoryTheory.Functor.Additive

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Preadditivestatement and proof · cited by 3,309
ComplexShapestatement and proof · cited by 1,684
CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
HomotopyCategorystatement · cited by 132
CategoryTheory.Functor.mapHomotopyCategorystatement · cited by 18
CategoryTheory.NatTrans.mapHomotopyCategorystatement and proof · cited by 3

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