Theorems · Theorem · algebraic topology

SSet.Truncated.HomotopyCategory.homMk_comp_homMk_assoc

∀ {V : SSet.Truncated 2}
  {x₀ x₁ x₂ : V.obj (Opposite.op { obj := { len := 0 }, property := SSet.OneTruncation₂._proof_1 })}
  {e₀₁ : SSet.Truncated.Edge x₀ x₁} {e₁₂ : SSet.Truncated.Edge x₁ x₂} {e₀₂ : SSet.Truncated.Edge x₀ x₂}
  (h : e₀₁.CompStruct e₁₂ e₀₂) {Z : V.HomotopyCategory} (h : SSet.Truncated.HomotopyCategory.mk x₂ ⟶ Z),
  CategoryTheory.CategoryStruct.comp (SSet.Truncated.HomotopyCategory.homMk e₀₁)
      (CategoryTheory.CategoryStruct.comp (SSet.Truncated.HomotopyCategory.homMk e₁₂) h) =
    CategoryTheory.CategoryStruct.comp (SSet.Truncated.HomotopyCategory.homMk e₀₂) h

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound