Theorems · Definition · category theory
CategoryTheory.nerve
(C : Type u) → [CategoryTheory.Category.{v, u} C] → SSetThe nerve of a category
- Cited by
- 68 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositeproof · cited by 8,081
- Opposite.unopproof · cited by 2,231
- SimplexCategoryproof · cited by 2,204
- SSetstatement · cited by 1,283
- Quiver.Hom.unopproof · cited by 903
- CategoryTheory.ComposableArrowsproof · cited by 627
- SimplexCategory.lenproof · cited by 542
- CategoryTheory.Cat.Hom.toFunctorproof · cited by 531
- TypeCat.ofHomproof · cited by 389
Cited by86
Results whose statement or proof uses this declaration.
- CategoryTheory.nerveMapstatement and proof · cited by 12
- CategoryTheory.nerve.homEquivstatement · cited by 11
- CategoryTheory.nerve.edgeMkstatement · cited by 9
- SSet.OneTruncation₂.nerveEquivstatement · cited by 8
- SSet.Truncated.HomotopyCategory.homToNerveMkstatement and proof · cited by 5
- SSet.OneTruncation₂.nerveHomEquivstatement and proof · cited by 4
- SSet.Truncated.HomotopyCategory.descOfTruncationstatement and proof · cited by 3
- PartialOrder.mem_nerve_nonDegenerate_iff_strictMonostatement and proof · cited by 3
- CategoryTheory.nerveFunctorproof · cited by 3
- CategoryTheory.Codiscrete.equivFunstatement and proof · cited by 3
- SSet.coherentIsoproof · cited by 3
- SSet.stdSimplex.isoNervestatement and proof · cited by 3