Theorems · Theorem · category theory

SSet.Truncated.HomotopyCategory.homToNerveMk_comp

∀ {X : SSet.Truncated 2} {C : Type u} [inst : CategoryTheory.SmallCategory C] {D : Type u}
  [inst_1 : CategoryTheory.SmallCategory D] (F : CategoryTheory.Functor X.HomotopyCategory C)
  (G : CategoryTheory.Functor C D),
  SSet.Truncated.HomotopyCategory.homToNerveMk (F.comp G) =
    CategoryTheory.CategoryStruct.comp (SSet.Truncated.HomotopyCategory.homToNerveMk F)
      ((SSet.truncation 2).map (CategoryTheory.nerveMap G))

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.SmallCategoryCategoryTheory.SmallCategory