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Theorems · Definition · algebraic topology

SSet.Truncated.Edge.CompStruct.compId

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

e : Edge x y is a composition of e with Edge.id y.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated
Cited by
7 results in Mathlib
Foundations
Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

SSet.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.HomotopicL.refl · cited by 1HomotopicL.reflSSet.Edge.CompStruct.compId · cited by 1CompStruct.compIdSSet.Truncated.HomotopyCategory.BinaryProduct.square · cited by 0BinaryProduct.squareSSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_homMk · cited by 0BinaryProduct.inverse_map…SSet.Truncated.HomotopicL.symm · cited by 0HomotopicL.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.EdgeSSet.Truncated.Edge.CompStruct · cited by 28Edge.CompStructSSet.Truncated.Edge.edge · cited by 27Edge.edgeSSet.Truncated.Edge.id · cited by 20Edge.idSimplexCategory.Truncated.σ₂ · cited by 20Truncated.σ₂CompStruct.compIdCITED BYCITES

Cites15

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

Cited by8

Results whose statement or proof uses this declaration.