Theorems · Definition · algebraic topology

SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompMapHomotopyCategorySndIso

(X Y : SSet.Truncated 2) →
  (SSet.Truncated.HomotopyCategory.BinaryProduct.inverse X Y).comp
      (SSet.Truncated.mapHomotopyCategory (CategoryTheory.SemiCartesianMonoidalCategory.snd X Y)) ≅
    CategoryTheory.Prod.snd X.HomotopyCategory Y.HomotopyCategory

The compatibility of HomotopyCategory.BinaryProduct.inverse with respect to the second projection.

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal
Cited by: 1 results in Mathlib
Foundations: Depth 78 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.

Cites22

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

CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Functorstatement · cited by 16,252
Oppositestatement · cited by 8,081
CategoryTheory.Functor.compstatement and proof · cited by 6,529
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
SimplexCategorystatement · cited by 2,204
CategoryTheory.Iso.reflproof · cited by 727
SimplexCategory.lenstatement · cited by 542
SimplexCategory.Truncatedstatement · cited by 236
SSet.Truncatedstatement and proof · cited by 214
CategoryTheory.SemiCartesianMonoidalCategory.sndstatement and proof · cited by 181

Cited by1

Results whose statement or proof uses this declaration.

SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_mapHomotopyCategory_sndproof · cited by 1