Theorems · Definition · algebraic topology
SSet.PtSimplex.relStructSuccEquivMulStruct
{X : SSet} →
{n : ℕ} →
{x : X.obj (Opposite.op { len := 0 })} →
{f g : X.PtSimplex n x} → {i : Fin n} → f.RelStruct g i.succ ≃ g.MulStruct SSet.RelativeMorphism.const f iIf f and g are in X.PtSimplex n x, then RelStruct f g i.succ
identifies to MulStruct g .const f i.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Equivstatement · cited by 8,337
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.stdSimplexstatement · cited by 499
- SSet.Subcomplex.toSSetstatement · cited by 315
- CategoryTheory.Subfunctor.objstatement · cited by 227
- SSet.boundarystatement · cited by 141
- SSet.Subcomplex.ofSimplexstatement · cited by 73
- SSet.conststatement · cited by 62
Cited by3
Results whose statement or proof uses this declaration.
- SSet.PtSimplex.MulStruct.mulOneproof · cited by 1
- SSet.PtSimplex.relStructSuccEquivMulStruct_apply_mapstatement and proof · cited by 0
- SSet.PtSimplex.relStructSuccEquivMulStruct_symm_apply_mapstatement and proof · cited by 0