Theorems · Theorem · algebraic topology

SSet.RelativeMorphism.Homotopy.precomp_h

∀ {X Y Z : SSet} {A : X.Subcomplex} {B : Y.Subcomplex} {φ : A.toSSet ⟶ B.toSSet} {C : Z.Subcomplex}
  {ψ : B.toSSet ⟶ C.toSSet} {f' g' : SSet.RelativeMorphism B C ψ} (h : f'.Homotopy g') (f : SSet.RelativeMorphism A B φ)
  {φψ : A.toSSet ⟶ C.toSSet} (fac : CategoryTheory.CategoryStruct.comp φ ψ = φψ),
  (h.precomp f fac).h =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight f.map (SSet.stdSimplex.obj { len := 1 })) h.h

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism

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Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound