Theorems · Definition · algebraic topology
SimplexCategory.sd
CategoryTheory.Functor SimplexCategory SSet
The functor SimplexCategory ⥤ SSet which sends ⦋n⦌ to the nerve of the
partially ordered type of nonempty finite chains in {0, ..., n} (ulifted to Type u).
Vertices in SimplexCategory.sd.obj ⦋n⦌ identify to nonempty subsets of {0, ..., n}.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement · cited by 8,081
- CategoryTheory.Functor.compproof · cited by 6,529
- SimplexCategorystatement · cited by 2,204
- SSetstatement · cited by 1,283
- SimplexCategory.toPartOrdproof · cited by 2
- PartOrd.nerveFunctorproof · cited by 2
- PartOrd.nonemptyFiniteChainsFunctorproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- SSet.stdSimplex.sdIsostatement and proof · cited by 0
- SSet.sdproof · cited by 0
- SSet.sdExAdjunctionproof · cited by 0
- SSet.exproof · cited by 0