Theorems · Theorem · algebraic topology

SSet.Truncated.HomotopyCategory.morphismProperty_eq_top

∀ {V : SSet.Truncated 2} {W : CategoryTheory.MorphismProperty V.HomotopyCategory} [W.IsMultiplicative],
  (∀ {x y : V.obj (Opposite.op { obj := { len := 0 }, property := SSet.OneTruncation₂._proof_1 })}
      (e : SSet.Truncated.Edge x y), W (SSet.Truncated.HomotopyCategory.homMk e)) →
    W = ⊤

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat

Cited by

0 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.MorphismProperty.IsMultiplicative