Theorems · Definition · algebraic topology
SSet.relativeCellComplex
(X : SSet) → HomotopicalAlgebra.RelativeCellComplex (fun n x => (SSet.boundary n).ι) ⊥.ι
If X is a simplicial set, then the inclusion (⊥ : SSet) ⟶ X of the empty
subcomplex of X is a relative cell complex with basic cells given by boundary
inclusions ∂Δ[d] ⟶ Δ[d], one for each nondegenerate d-simplex of X.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- Bot.botstatement and proof · cited by 4,720
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.stdSimplexstatement · cited by 499
- SSet.Subcomplexstatement · cited by 461
- SSet.Subcomplex.toSSetstatement · cited by 315
- SSet.boundarystatement · cited by 141
- SSet.Subcomplex.ιstatement and proof · cited by 136
- SSet.relativeCellComplexOfMonoproof · cited by 14
- HomotopicalAlgebra.RelativeCellComplexstatement · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- SSet.relativeCellComplexCellsEquivstatement and proof · cited by 3
- SSet.relativeCellComplexCellsEquiv_applystatement and proof · cited by 0
- SSet.relativeCellComplexCellsEquiv_symm_apply_jstatement · cited by 0
- SSet.relativeCellComplexCellsEquiv_symm_apply_k_simplexstatement · cited by 0