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Theorems · Definition · algebraic topology

SSet.RelativeMorphism.HomotopyClass.precomp

{X Y Z : SSet} →
  {A : X.Subcomplex} →
    {B : Y.Subcomplex} →
      {φ : A.toSSet ⟶ B.toSSet} →
        {C : Z.Subcomplex} →
          {ψ : B.toSSet ⟶ C.toSSet} →
            SSet.RelativeMorphism.HomotopyClass B C ψ →
              SSet.RelativeMorphism A B φ →
                {φψ : A.toSSet ⟶ C.toSSet} →
                  CategoryTheory.CategoryStruct.comp φ ψ = φψ → SSet.RelativeMorphism.HomotopyClass A C φψ

The precomposition of an homotopy class with a relative morphism.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism
Cited by
1 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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SSet.RelativeMorphism.precomp_homotopyClass · cited by 0RelativeMorphism.precomp_…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetSSet.Subcomplex · cited by 461SSet.SubcomplexSSet.Subcomplex.toSSet · cited by 315Subcomplex.toSSetSSet.RelativeMorphism · cited by 39SSet.RelativeMorphismSSet.RelativeMorphism.comp · cited by 6RelativeMorphism.compSSet.RelativeMorphism.homotopyClass · cited by 4RelativeMorphism.homotopy…SSet.RelativeMorphism.HomotopyClass · cited by 4RelativeMorphism.Homotopy…HomotopyClass.precompCITED BYCITES

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