Theorems · Definition · algebraic topology
SSet.StrictSegal.spineToDiagonal
{X : SSet} → X.StrictSegal → {n : ℕ} → X.Path n → X.obj (Opposite.op { len := 1 })In the presence of the strict Segal condition, a path of length n can be
"composed" by taking the diagonal edge of the resulting n-simplex.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Pathstatement and proof · cited by 46
- SSet.StrictSegalstatement and proof · cited by 25
- SSet.StrictSegal.spineToSimplexproof · cited by 16
- CategoryTheory.SimplicialObject.diagonalproof · cited by 0
Cited by3
Results whose statement or proof uses this declaration.
- SSet.StrictSegal.spine_δ_arrow_eqstatement and proof · cited by 1
- SSet.StrictSegal.spineToSimplex_edgestatement · cited by 1
- SSet.StrictSegal.quasicategoryproof · cited by 0