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Theorems · Theorem · algebraic topology

SSet.Subcomplex.Pairing.RankFunction.isPullback

∀ {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [inst : LinearOrder ι] (f : P.RankFunction ι)
  [inst_1 : P.IsProper] [inst_2 : SuccOrder ι] [inst_3 : NoMaxOrder ι] (j : ι),
  CategoryTheory.IsPullback (f.t j) (f.m j) (SSet.Subcomplex.homOfLE ⋯) (f.b j)
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
Cited by
1 results in Mathlib
Foundations
Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderSSet.Subcomplex.Pairing.IsProperSuccOrderNoMaxOrder
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Around this declaration

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

SSet.Subcomplex.Pairing.RankFunction.isPushout · cited by 0RankFunction.isPushoutDFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapLinearOrder · cited by 8572LinearOrderOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appSet.Elem · cited by 7166Set.ElemCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homEquiv.symm · cited by 3681Equiv.symmSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetCategoryTheory.Limits.IsLimit · cited by 664Limits.IsLimitOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderSSet.stdSimplex · cited by 499SSet.stdSimplexRankFunction.isPullbackCITED BYCITES

Cites59

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