Theorems · Theorem · algebraic topology
SSet.Subcomplex.preimage_obj
∀ {X Y : SSet} (A : X.Subcomplex) (p : Y ⟶ X) (n : SimplexCategoryᵒᵖ),
(A.preimage p).obj n = ⇑(CategoryTheory.ConcreteCategory.hom (p.app n)) ⁻¹' A.obj n- Cited by
- 11 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.NatTrans.appstatement · cited by 7,406
- Set.preimagestatement · cited by 4,946
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- SimplexCategorystatement and proof · cited by 2,204
- TypeCat.Funstatement · cited by 1,307
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
Cited by11
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.image_le_iffproof · cited by 6
- SSet.Subcomplex.unionProd.preimage_β_homproof · cited by 2
- SSet.Subcomplex.image_ofSimplexproof · cited by 1
- SSet.relativeCellComplexOfMono.isPullbackproof · cited by 1
- SSet.Subcomplex.preimage_image_of_isIsoproof · cited by 1
- SSet.Subcomplex.preimage_invproof · cited by 0
- SSet.Subcomplex.preimage_ιproof · cited by 0
- SSet.op_boundaryproof · cited by 0
- SSet.op_hornproof · cited by 0
- SSet.Subcomplex.preimage_iInfproof · cited by 0
- SSet.Subcomplex.preimage_iSupproof · cited by 0