Theorems · Definition · category theory
CategoryTheory.SimplicialObject.const
(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Functor C (CategoryTheory.SimplicialObject C)The constant simplicial object is the constant functor.
- Cited by
- 110 results in Mathlib
- Foundations
- Depth 31 from the axioms, rests on 297 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- SimplexCategorystatement and proof · cited by 2,204
- CategoryTheory.Functor.constproof · cited by 1,264
- CategoryTheory.SimplicialObjectstatement · cited by 548
Cited by123
Results whose statement or proof uses this declaration.
- CategoryTheory.SimplicialObject.Augmentedproof · cited by 113
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.sstatement · cited by 13
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'statement · cited by 11
- CategoryTheory.SimplicialObject.Augmented.dropproof · cited by 10
- CategoryTheory.SimplicialObject.Augmented.pointproof · cited by 10
- CategoryTheory.SimplicialObject.Augmented.constproof · cited by 7
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.section_statement · cited by 7
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.homotopy.hstatement · cited by 3
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_εstatement · cited by 2
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.section_app_comp_hom_appstatement · cited by 2
- CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.homotopystatement · cited by 1
- CategoryTheory.SimplicialObject.augment_hom_appstatement · cited by 1