Theorems · Theorem · algebraic topology

SSet.hasDimensionLT_prod

∀ (X₁ X₂ : SSet) (d₁ d₂ : ℕ) [X₁.HasDimensionLT d₁] [X₂.HasDimensionLT d₂] (n : ℕ),
  autoParam (d₁ + d₂ ≤ n + 1) SSet.hasDimensionLT_prod._auto_1 →
    (CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ X₂).HasDimensionLT n

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd
Cited by: 1 results in Mathlib
Foundations: Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SSet.HasDimensionLT SSet.HasDimensionLT

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites25

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

DFunLike.coeproof · cited by 62,936
CategoryTheory.Functor.objproof · cited by 19,642
Oppositestatement · cited by 8,081
Equiv.symmproof · cited by 3,681
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
iSupproof · cited by 2,415
SimplexCategorystatement · cited by 2,204
SSetstatement and proof · cited by 1,283
CategoryTheory.MonoidalCategoryStruct.tensorHomproof · cited by 587
SSet.stdSimplexproof · cited by 499
SSet.Subcomplexproof · cited by 461
SSet.Subcomplex.toSSetproof · cited by 315

Cited by1

Results whose statement or proof uses this declaration.

SSet.hasDimensionLE_prodproof · cited by 0