Theorems · Theorem · algebraic topology

SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_homMk

∀ {X Y : SSet.Truncated 2}
  {x₀ x₁ : X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge.tensor._proof_1 })}
  (e : SSet.Truncated.Edge x₀ x₁)
  {y₀ y₁ : Y.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge.tensor._proof_1 })}
  (e' : SSet.Truncated.Edge y₀ y₁),
  (SSet.Truncated.HomotopyCategory.BinaryProduct.inverse X Y).map
      (CategoryTheory.Prod.mkHom (SSet.Truncated.HomotopyCategory.homMk e) (SSet.Truncated.HomotopyCategory.homMk e')) =
    SSet.Truncated.HomotopyCategory.homMk (e.tensor e')

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound