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Theorems · Definition · algebraic topology

SSet.Truncated.Edge.id

{X : SSet.Truncated 2} →
  (x : X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge._proof_1 })) → SSet.Truncated.Edge x x

The constant edge on a 0-simplex.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated
Cited by
20 results in Mathlib
Foundations
Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

SSet.Edge.id · cited by 24Edge.idSSet.Truncated.Edge.CompStruct.idComp · cited by 10CompStruct.idCompSSet.Truncated.HomotopicL · cited by 8Truncated.HomotopicLSSet.Truncated.Edge.CompStruct.compId · cited by 7CompStruct.compIdSSet.Truncated.HomotopicR · cited by 7Truncated.HomotopicRSSet.Truncated.HomotopyCategory.lift · cited by 2HomotopyCategory.liftSSet.Truncated.HomotopicL.homotopicR · cited by 2HomotopicL.homotopicRSSet.Truncated.HomotopicR.homotopicL · cited by 2HomotopicR.homotopicLSSet.Truncated.Edge.CompStruct.comp_unique · cited by 1CompStruct.comp_uniqueSSet.Truncated.Edge.CompStruct.idCompId · cited by 1CompStruct.idCompIdSSet.Truncated.Edge.CompStruct.idCompId_simplex · cited by 1CompStruct.idCompId_simpl…SSet.Truncated.Edge.id_edge · cited by 1Edge.id_edgeSSet.OneTruncation₂.reflQuiver_id · cited by 1OneTruncation₂.reflQuiver…SSet.Truncated.Edge.map_id · cited by 1Edge.map_idSSet.Truncated.HomotopicR.symm · cited by 0HomotopicR.symmDFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homSimplexCategory · cited by 2204SimplexCategoryQuiver.Hom.op · cited by 1948Hom.opSimplexCategory.len · cited by 542SimplexCategory.lenSimplexCategory.Truncated · cited by 236SimplexCategory.TruncatedSSet.Truncated · cited by 214SSet.TruncatedSSet.Truncated.Edge · cited by 81Truncated.EdgeSimplexCategory.Truncated.σ₂ · cited by 20Truncated.σ₂Edge.idCITED BYCITES

Cites12

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

Cited by28

Results whose statement or proof uses this declaration.