Theorems · Definition · algebraic topology
SSet.Subcomplex.fromPreimage
{X Y : SSet} → (A : X.Subcomplex) → (p : Y ⟶ X) → (A.preimage p).toSSet ⟶ A.toSSetGiven a morphism of simplicial sets p : Y ⟶ X and
A : X.Subcomplex, this is the induced morphism
(A.preimage p : SSet) ⟶ (A : SSet).
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 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.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
- SSet.Subcomplex.toSSetstatement · cited by 315
- SSet.Subcomplex.ιproof · cited by 136
- SSet.Subcomplex.preimagestatement and proof · cited by 37
- SSet.Subcomplex.liftproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.fromPreimage_ιstatement · cited by 1
- SSet.Subcomplex.fromPreimage_app_hom_apply_coestatement and proof · cited by 0
- SSet.Subcomplex.fromPreimage_ι_assocstatement and proof · cited by 0