Theorems · Theorem · algebraic topology

SSet.Truncated.HomotopyCategory.BinaryProduct.left_unitality

∀ (X Y : SSet.Truncated 2)
  [inst : Unique (X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge.tensor._proof_1 }))]
  [inst_1 :
    Subsingleton
      (X.obj (Opposite.op { obj := { len := 1 }, property := SSet.Truncated.HomotopyCategory.isoTerminal._proof_1 }))],
  CategoryTheory.Prod.snd (↑CategoryTheory.Cat.chosenTerminal) Y.HomotopyCategory =
    ((SSet.Truncated.HomotopyCategory.isoTerminal X).inv.toFunctor.prod
          (CategoryTheory.Functor.id Y.HomotopyCategory)).comp
      ((SSet.Truncated.HomotopyCategory.BinaryProduct.inverse X Y).comp
        (SSet.Truncated.mapHomotopyCategory (CategoryTheory.SemiCartesianMonoidalCategory.snd X Y)))

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniqueSubsingleton