Theorems · Definition · algebraic topology
SSet.RelativeMorphism.comp
{X Y Z : SSet} →
{A : X.Subcomplex} →
{B : Y.Subcomplex} →
{φ : A.toSSet ⟶ B.toSSet} →
SSet.RelativeMorphism A B φ →
{C : Z.Subcomplex} →
{ψ : B.toSSet ⟶ C.toSSet} →
SSet.RelativeMorphism B C ψ →
{φψ : A.toSSet ⟶ C.toSSet} → CategoryTheory.CategoryStruct.comp φ ψ = φψ → SSet.RelativeMorphism A C φψThe composition of relative morphisms.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
- SSet.Subcomplex.toSSetstatement and proof · cited by 315
- SSet.RelativeMorphism.mapproof · cited by 51
- SSet.RelativeMorphismstatement and proof · cited by 39
Cited by10
Results whose statement or proof uses this declaration.
- SSet.RelativeMorphism.HomotopyClass.postcompproof · cited by 1
- SSet.RelativeMorphism.HomotopyClass.precompproof · cited by 1
- SSet.RelativeMorphism.Homotopy.postcompstatement · cited by 1
- SSet.RelativeMorphism.Homotopy.precompstatement · cited by 1
- SSet.RelativeMorphism.comp_mapstatement and proof · cited by 0
- SSet.RelativeMorphism.comp.congr_simpstatement and proof · cited by 0
- SSet.RelativeMorphism.postcomp_homotopyClassstatement · cited by 0
- SSet.RelativeMorphism.precomp_homotopyClassstatement · cited by 0
- SSet.RelativeMorphism.Homotopy.postcomp_hstatement · cited by 0
- SSet.RelativeMorphism.Homotopy.precomp_hstatement · cited by 0