Theorems · Definition · category theory
AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
AugmentedSimplexCategory.equivAugmentedSimplicialObject.functor.comp
CategoryTheory.SimplicialObject.Augmented.drop ≅
(CategoryTheory.Functor.whiskeringLeft SimplexCategoryᵒᵖ AugmentedSimplexCategoryᵒᵖ C).obj
AugmentedSimplexCategory.inclusion.opThrough the equivalence (AugmentedSimplexCategoryᵒᵖ ⥤ C) ≌ SimplicialObject.Augmented C,
dropping the augmentation corresponds to precomposition with
inclusionᵒᵖ : SimplexCategoryᵒᵖ ⥤ AugmentedSimplexCategoryᵒᵖ.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 44 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.
Cites17
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.objstatement · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement · cited by 8,081
- CategoryTheory.Functor.compstatement and proof · cited by 6,529
- CategoryTheory.Isostatement · cited by 3,963
- SimplexCategorystatement · cited by 2,204
- CategoryTheory.Equivalence.functorstatement and proof · cited by 1,268
- CategoryTheory.Functor.opstatement · cited by 997
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.SimplicialObjectstatement · cited by 548
- CategoryTheory.Functor.whiskeringLeftstatement · cited by 395
Cited by2
Results whose statement or proof uses this declaration.
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_appstatement and proof · cited by 0
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_appstatement and proof · cited by 0