Mathlib Map

Theorems · Definition · algebraic topology

SSet.Edge.InvStruct.homInvId

{X : SSet} →
  {x₀ x₁ : X.obj (Opposite.op { len := 0 })} →
    {hom : SSet.Edge x₀ x₁} → (self : hom.InvStruct) → hom.CompStruct self.inv (SSet.Edge.id x₀)

The simplex witnessing that hom and inv compose to the identity

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.CompStruct
Cited by
8 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SSet.Edge.InvStruct.map · cited by 3InvStruct.mapSSet.Edge.InvStruct.ofEq · cited by 3InvStruct.ofEqSSet.Edge.InvStruct.invStructInv · cited by 3InvStruct.invStructInvSSet.Edge.InvStruct.ext · cited by 1InvStruct.extSSet.Edge.InvStruct.invStructInv_invHomId · cited by 0InvStruct.invStructInv_in…SSet.Edge.InvStruct.map_homInvId · cited by 0InvStruct.map_homInvIdSSet.coherentIso.invStructHom_homInvId · cited by 0coherentIso.invStructHom_…SSet.Edge.InvStruct.ofEq_homInvId · cited by 0InvStruct.ofEq_homInvIdSSet.Edge.InvStruct.ext_iff · cited by 0InvStruct.ext_iffSSet.Edge.InvStruct.invStructId_homInvId · cited by 0InvStruct.invStructId_hom…SSet.Edge.InvStruct.invStructInv_homInvId · cited by 0InvStruct.invStructInv_ho…CategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetSSet.Edge · cited by 55SSet.EdgeSSet.Edge.CompStruct · cited by 25Edge.CompStructSSet.Edge.id · cited by 24Edge.idSSet.Edge.InvStruct · cited by 14Edge.InvStructSSet.Edge.InvStruct.inv · cited by 13InvStruct.invInvStruct.homInvIdCITED BYCITES

Cites9

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

Cited by11

Results whose statement or proof uses this declaration.