Theorems · Definition · category theory
SimplexCategory.toCat
CategoryTheory.Functor SimplexCategory CategoryTheory.Cat
This functor SimplexCategory ⥤ Cat sends ⦋n⦌ (for n : ℕ)
to the category attached to the ordered set {0, 1, ..., n}
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.compproof · cited by 6,529
- SimplexCategorystatement · cited by 2,204
- CategoryTheory.Catstatement · cited by 884
- CategoryTheory.forget₂proof · cited by 260
- PartOrdproof · cited by 65
- LinOrdproof · cited by 46
- Latproof · cited by 43
- Preordproof · cited by 42
- NonemptyFinLinOrdproof · cited by 27
- SimplexCategory.skeletalFunctorproof · cited by 7
- preordToCatproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.nerveproof · cited by 68
- CategoryTheory.nerve_mapstatement · cited by 0
- SimplexCategory.toCat_mapstatement and proof · cited by 0
- SimplexCategory.toCat_objstatement and proof · cited by 0
- SimplexCategory.toCat.obj_eq_Finstatement · cited by 0