Theorems · Definition · algebraic topology

SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso

(X Y : SSet.Truncated 2) →
  (SSet.Truncated.HomotopyCategory.BinaryProduct.inverse X Y).comp
      (SSet.Truncated.HomotopyCategory.BinaryProduct.functor X Y) ≅
    CategoryTheory.Functor.id (X.HomotopyCategory × Y.HomotopyCategory)

Auxiliary definition for equivalence.

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal
Cited by: 3 results in Mathlib
Foundations: Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites21

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.Functor.idstatement · cited by 3,333
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

Cited by4

Results whose statement or proof uses this declaration.

SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_appstatement · cited by 0
SSet.Truncated.HomotopyCategory.BinaryProduct.equivalenceproof · cited by 0
SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_functorproof · cited by 0
SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_appstatement · cited by 0