Theorems · Definition · algebraic topology
SSet.relativeCellComplexOfMono.sigmaStdSimplex
{X Y : SSet} → (X ⟶ Y) → ℕ → SSetIf i : X ⟶ Y is a monomorphism of simplicial sets and d : ℕ, this is
a coproduct of copies of Δ[d] indexed by the nondegenerate d-simplices of Y
not in the range of i.
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Functor.objproof · cited by 19,642
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.stdSimplexproof · cited by 499
- CategoryTheory.Limits.sigmaObjproof · cited by 302
- SSet.relativeCellComplexOfMono.Cellproof · cited by 29
Cited by20
Results whose statement or proof uses this declaration.
- SSet.relativeCellComplexOfMono.bstatement · cited by 12
- SSet.relativeCellComplexOfMono.Cell.ιSigmaStdSimplexstatement · cited by 12
- SSet.relativeCellComplexOfMono.lstatement · cited by 8
- SSet.relativeCellComplexOfMono.wstatement · cited by 3
- SSet.relativeCellComplexOfMono.Cell.ι_lstatement · cited by 3
- SSet.relativeCellComplexOfMono.Cell.b_app_ι_app_objEquiv_symm_valstatement · cited by 2
- SSet.relativeCellComplexOfMono.Cell.ι_b_ιstatement · cited by 2
- SSet.relativeCellComplexOfMono.ιSigmaStdSimplex_jointly_surjectivestatement and proof · cited by 2
- SSet.relativeCellComplexOfMono.Cell.ι_t_ι_eq_ι_l_b_ιstatement · cited by 2
- SSet.relativeCellComplexOfMono.isPullbackstatement and proof · cited by 1
- SSet.relativeCellComplexOfMono.isPushout_auxstatement and proof · cited by 1
- SSet.relativeCellComplexOfMono.range_r_app_union_range_b_appstatement · cited by 1