Theorems · Definition · algebraic topology

SSet.RelativeMorphism.Homotopy.postcomp

{X Y Z : SSet} →
  {A : X.Subcomplex} →
    {B : Y.Subcomplex} →
      {φ : A.toSSet ⟶ B.toSSet} →
        {f g : SSet.RelativeMorphism A B φ} →
          {C : Z.Subcomplex} →
            {ψ : B.toSSet ⟶ C.toSSet} →
              f.Homotopy g →
                (f' : SSet.RelativeMorphism B C ψ) →
                  {φψ : A.toSSet ⟶ C.toSSet} →
                    (fac : CategoryTheory.CategoryStruct.comp φ ψ = φψ) → (f.comp f' fac).Homotopy (g.comp f' fac)

The postcomposition of an homotopy with a relative morphism.

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism

Cited by

1 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound