Theorems · Theorem · algebraic topology

SSet.Truncated.Edge.CompStruct.tensor_simplex_fst

∀ {X Y : SSet.Truncated 2}
  {x₀ x₁ x₂ : X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge.tensor._proof_1 })}
  {e₀₁ : SSet.Truncated.Edge x₀ x₁} {e₁₂ : SSet.Truncated.Edge x₁ x₂} {e₀₂ : SSet.Truncated.Edge x₀ x₂}
  (hx : e₀₁.CompStruct e₁₂ e₀₂)
  {y₀ y₁ y₂ : Y.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge.tensor._proof_1 })}
  {e'₀₁ : SSet.Truncated.Edge y₀ y₁} {e'₁₂ : SSet.Truncated.Edge y₁ y₂} {e'₀₂ : SSet.Truncated.Edge y₀ y₂}
  (hy : e'₀₁.CompStruct e'₁₂ e'₀₂), (hx.tensor hy).simplex.1 = hx.simplex

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal

Cited by

0 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound