Theorems · Definition · algebraic topology
SSet.skeletonOfMono
{X Y : SSet} → (X ⟶ Y) → ℕ →o Y.SubcomplexThe skeleton of a monomorphism i : X ⟶ Y of simplicial sets.
It sends n : ℕ to Subcomplex.range i ⊔ Y.skeleton n.
See SSet.relativeCellComplexOfMono for the main result regarding
this definition.
(Even though [Mono i] is technically not required in this definition,
the intended use of this definition and the corresponding API is
when [Mono i] holds.)
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 69 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.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- OrderHomstatement · cited by 934
- SSet.Subcomplexstatement · cited by 461
- SSet.Subcomplex.rangeproof · cited by 49
- SSet.skeletonproof · cited by 11
Cited by36
Results whose statement or proof uses this declaration.
- SSet.relativeCellComplexOfMono.bstatement · cited by 12
- SSet.relativeCellComplexOfMono.tstatement · cited by 7
- SSet.relativeCellComplexOfMono.rstatement · cited by 6
- SSet.relativeCellComplexOfMono.Cell.range_map_lestatement and proof · cited by 3
- SSet.relativeCellComplexOfMono.wstatement and proof · cited by 3
- SSet.relativeCellComplexOfMono.Cell.b_app_ι_app_objEquiv_symm_valstatement · cited by 2
- SSet.relativeCellComplexOfMono.Cell.ι_b_ιstatement and proof · cited by 2
- SSet.relativeCellComplexOfMono.Cell.ι_t_ι_eq_ι_l_b_ιstatement and proof · cited by 2
- SSet.relativeCellComplexOfMono.isPullbackstatement and proof · cited by 1
- SSet.relativeCellComplexOfMono.Cell.preimage_mapstatement and proof · cited by 1
- SSet.relativeCellComplexOfMono.range_r_app_union_range_b_appstatement and proof · cited by 1
- SSet.skeletonOfMono_obj_eq_topstatement and proof · cited by 1