Theorems · Theorem · algebraic topology

SSet.Truncated.Edge.CompStruct.map_simplex

∀ {X Y : SSet.Truncated 2}
  {x₀ x₁ x₂ : X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge._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) (f : X ⟶ Y),
  (h.map f).simplex =
    (CategoryTheory.ConcreteCategory.hom
        (f.app (Opposite.op { obj := { len := 2 }, property := SSet.Truncated.Edge.CompStruct._proof_1 })))
      h.simplex

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound