Theorems · Definition · category theory
CategoryTheory.SimplicialObject.Augmented
(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type (max u v)The category of augmented simplicial objects, defined as a comma category.
- Cited by
- 113 results in Mathlib
- Foundations
- Depth 32 from the axioms, rests on 300 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Functor.idproof · cited by 3,333
- CategoryTheory.Commaproof · cited by 566
- CategoryTheory.SimplicialObjectproof · cited by 548
- CategoryTheory.SimplicialObject.constproof · cited by 110
Cited by161
Results whose statement or proof uses this declaration.
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracystatement · cited by 24
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectstatement · cited by 23
- CategoryTheory.Arrow.augmentedCechNervestatement · cited by 16
- CategoryTheory.SimplicialObject.Augmented.rightOpstatement and proof · cited by 15
- CategoryTheory.SimplicialObject.Augmented.toArrowstatement and proof · cited by 15
- CategoryTheory.CosimplicialObject.Augmented.leftOpstatement · cited by 14
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.sstatement and proof · cited by 13
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'statement and proof · cited by 11
- CategoryTheory.SimplicialObject.Augmented.dropstatement · cited by 10
- CategoryTheory.SimplicialObject.Augmented.pointstatement · cited by 10
- CategoryTheory.SimplicialObject.augmentedCechNervestatement · cited by 7
- CategoryTheory.SimplicialObject.Augmented.conststatement · cited by 7