Theorems · Definition · algebraic topology

SSet.prodStdSimplex.isoNerve

(p q : ℕ) →
  CategoryTheory.MonoidalCategoryStruct.tensorObj (SSet.stdSimplex.obj { len := p })
      (SSet.stdSimplex.obj { len := q }) ≅
    CategoryTheory.nerve (ULift.{u, 0} (Fin (p + 1) × Fin (q + 1)))

The binary product Δ[p] ⊗ Δ[q] identifies to the nerve of ULift (Fin (p + 1) × Fin (q + 1)).

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex
Cited by: 2 results in Mathlib
Foundations: Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites18

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

CategoryTheory.Functor.objstatement and proof · cited by 19,642
Oppositestatement and proof · cited by 8,081
CategoryTheory.Isostatement and proof · cited by 3,963
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
SimplexCategorystatement and proof · cited by 2,204
SSetstatement · cited by 1,283
OrderHomproof · cited by 934
SSet.stdSimplexstatement and proof · cited by 499
Equiv.transproof · cited by 337
CategoryTheory.NatIso.ofComponentsproof · cited by 178
CategoryTheory.nervestatement and proof · cited by 68
Monotone.functorproof · cited by 66

Cited by2

Results whose statement or proof uses this declaration.

SSet.prodStdSimplex.nonDegenerate_iff_strictMono_objEquivproof · cited by 3
SSet.prodStdSimplex.nonDegenerate_iff_injective_objEquivproof · cited by 1