Theorems · Theorem · algebraic topology

SSet.Truncated.HomotopyCategory.BinaryProduct.square

∀ {X Y : SSet.Truncated 2}
  {x₀ x₁ : X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge.tensor._proof_1 })}
  (ex : SSet.Truncated.Edge x₀ x₁)
  {y₀ y₁ : Y.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge.tensor._proof_1 })}
  (ey : SSet.Truncated.Edge y₀ y₁),
  CategoryTheory.CategoryStruct.comp (SSet.Truncated.HomotopyCategory.homMk (ex.tensor (SSet.Truncated.Edge.id y₀)))
      (SSet.Truncated.HomotopyCategory.homMk ((SSet.Truncated.Edge.id x₁).tensor ey)) =
    CategoryTheory.CategoryStruct.comp (SSet.Truncated.HomotopyCategory.homMk ((SSet.Truncated.Edge.id x₀).tensor ey))
      (SSet.Truncated.HomotopyCategory.homMk (ex.tensor (SSet.Truncated.Edge.id y₁)))

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal

Cited by

0 results in Mathlib

Foundations

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