Mathlib Map

Theorems · Definition · algebraic topology

SSet.Truncated.HomotopyCategory.mk

{V : SSet.Truncated 2} →
  V.obj (Opposite.op { obj := { len := 0 }, property := SSet.OneTruncation₂._proof_1 }) → V.HomotopyCategory

Constructor for objects of the homotopy category of a 2-truncated simplicial set.

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

Around this declaration

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

SSet.Truncated.HomotopyCategory.homMk · cited by 24HomotopyCategory.homMkSSet.Truncated.HomotopyCategory.mkNatIso · cited by 5HomotopyCategory.mkNatIsoSSet.Truncated.HomotopyCategory.homToNerveMk · cited by 5HomotopyCategory.homToNer…SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso · cited by 3BinaryProduct.functorComp…SSet.Truncated.HomotopyCategory.homMk_comp_homMk · cited by 3HomotopyCategory.homMk_co…SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso · cited by 3BinaryProduct.inverseComp…SSet.Truncated.HomotopyCategory.mkNatTrans · cited by 2HomotopyCategory.mkNatTra…SSet.Truncated.HomotopyCategory.mk_surjective · cited by 2HomotopyCategory.mk_surje…SSet.Truncated.HomotopyCategory.congr_arrowMk_homMk · cited by 1HomotopyCategory.congr_ar…SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk · cited by 1HomotopyCategory.descOfTr…SSet.Truncated.HomotopyCategory.functor_ext · cited by 1HomotopyCategory.functor_…SSet.Truncated.HomotopyCategory.homToNerveMk_app_edge · cited by 1HomotopyCategory.homToNer…SSet.Truncated.HomotopyCategory.homToNerveMk_app_one · cited by 1HomotopyCategory.homToNer…SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompMapHomotopyCategoryFstIso · cited by 1BinaryProduct.inverseComp…SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompMapHomotopyCategorySndIso · cited by 1BinaryProduct.inverseComp…CategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategorySimplexCategory.len · cited by 542SimplexCategory.lenSimplexCategory.Truncated · cited by 236SimplexCategory.TruncatedSSet.Truncated · cited by 214SSet.TruncatedSSet.Truncated.HomotopyCategory · cited by 54Truncated.HomotopyCategoryCategoryTheory.Cat.FreeRefl.mk · cited by 17FreeRefl.mkSSet.Truncated.HomotopyCategory.quotientFunctor · cited by 5HomotopyCategory.quotient…HomotopyCategory.mkCITED BYCITES

Cites9

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Cited by49

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