Theorems · Theorem · algebraic topology

SSet.Truncated.HomotopyCategory.congr_arrowMk_homMk

∀ {V : SSet.Truncated 2} {x₀ x₁ : V.obj (Opposite.op { obj := { len := 0 }, property := SSet.OneTruncation₂._proof_1 })}
  (e : SSet.Truncated.Edge x₀ x₁)
  {y₀ y₁ : V.obj (Opposite.op { obj := { len := 0 }, property := SSet.OneTruncation₂._proof_1 })}
  (e' : SSet.Truncated.Edge y₀ y₁),
  e.edge = e'.edge →
    CategoryTheory.Arrow.mk (SSet.Truncated.HomotopyCategory.homMk e) =
      CategoryTheory.Arrow.mk (SSet.Truncated.HomotopyCategory.homMk e')

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat

Cited by

1 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound