Theorems · Definition · category theory
CategoryTheory.SimplicialObject
(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type (max v u)The category of simplicial objects valued in a category C.
This is the category of contravariant functors from SimplexCategory to C.
- Cited by
- 548 results in Mathlib
- Foundations
- Depth 30 from the axioms, rests on 261 definitions · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- CategoryTheory.Functorproof · cited by 16,252
- Oppositeproof · cited by 8,081
- SimplexCategoryproof · cited by 2,204
Cited by740
Results whose statement or proof uses this declaration.
- SSetproof · cited by 1,283
- CategoryTheory.SimplicialObject.δstatement and proof · cited by 188
- AlgebraicTopology.AlternatingFaceMapComplex.objstatement and proof · cited by 146
- CategoryTheory.SimplicialObject.Augmentedproof · cited by 113
- CategoryTheory.SimplicialObject.conststatement · cited by 110
- CategoryTheory.SimplicialObject.σstatement and proof · cited by 106
- AlgebraicTopology.DoldKan.PInftystatement and proof · cited by 94
- CategoryTheory.SimplicialObject.Splitting.Nstatement and proof · cited by 81
- CategoryTheory.SimplicialObject.Splittingstatement · cited by 59
- CategoryTheory.SimplicialObject.Splitting.cofanstatement and proof · cited by 46
- AlgebraicTopology.DoldKan.N₁statement and proof · cited by 43
- AlgebraicTopology.DoldKan.Pstatement and proof · cited by 38
Showing the 200 most cited of 740.