Theorems · Definition · algebraic topology
SSet.Truncated.HomotopyCategory.quotientFunctor
(V : SSet.Truncated 2) → CategoryTheory.Functor (CategoryTheory.Cat.FreeRefl (SSet.OneTruncation₂ V)) V.HomotopyCategory
A canonical functor from the free category on the refl quiver underlying a 2-truncated
simplicial set V to its homotopy category.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functorstatement · cited by 16,252
- SSet.Truncatedstatement and proof · cited by 214
- SSet.Truncated.HomotopyCategorystatement · cited by 54
- CategoryTheory.Quotient.functorproof · cited by 41
- CategoryTheory.Cat.FreeReflstatement · cited by 34
- SSet.OneTruncation₂statement · cited by 26
- SSet.OneTruncation₂.HoRel₂proof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- SSet.Truncated.HomotopyCategory.mkproof · cited by 37
- SSet.Truncated.HomotopyCategory.homMkproof · cited by 24
- SSet.Truncated.mapHomotopyCategoryproof · cited by 13
- SSet.Truncated.HomotopyCategory.morphismPropertyHomMk_eq_strictMapstatement and proof · cited by 1
- SSet.Truncated.hoFunctor₂_naturalitystatement · cited by 0
- SSet.Truncated.HomotopyCategory.homMk_idproof · cited by 0
- SSet.Truncated.HomotopyCategory.lift_unique'statement and proof · cited by 0