Mathlib Map

Theorems · Definition · algebraic topology

SSet.Subcomplex.preimage

{X Y : SSet} → X.Subcomplex → (Y ⟶ X) → Y.Subcomplex

The preimage of a subcomplex by a morphism of simplicial sets.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex
Cited by
37 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SSet.Subcomplex.preimage_obj · cited by 11Subcomplex.preimage_objSSet.Subcomplex.N.orderIsoOfIso · cited by 8N.orderIsoOfIsoSSet.Subcomplex.Pairing.ofIso · cited by 7Pairing.ofIsoSSet.Subcomplex.image_le_iff · cited by 6Subcomplex.image_le_iffSSet.Subcomplex.fromPreimage · cited by 3Subcomplex.fromPreimageSSet.Subcomplex.Pairing.ofIso_p · cited by 2Pairing.ofIso_pSSet.Subcomplex.unionProd.preimage_β_hom · cited by 2unionProd.preimage_β_homSSet.Subcomplex.preimage_range · cited by 1Subcomplex.preimage_rangeSSet.Subcomplex.Pairing.RankFunction.Cell.preimage_filtration_map · cited by 1Cell.preimage_filtration_…SSet.relativeCellComplexOfMono.Cell.preimage_map · cited by 1Cell.preimage_mapSSet.Subcomplex.fromPreimage_ι · cited by 1Subcomplex.fromPreimage_ιSSet.Subcomplex.image_ofSimplex · cited by 1Subcomplex.image_ofSimplexSSet.Subcomplex.image_preimage_le · cited by 1Subcomplex.image_preimage…SSet.Subcomplex.preimage_image_of_isIso · cited by 1Subcomplex.preimage_image…SSet.Subcomplex.preimage_inv · cited by 0Subcomplex.preimage_invDFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appSet.preimage · cited by 4946Set.preimageCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetSSet.Subcomplex · cited by 461SSet.SubcomplexCategoryTheory.Subfunctor.obj · cited by 227Subfunctor.objSubcomplex.preimageCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by40

Results whose statement or proof uses this declaration.