Theorems · Definition · category theory
AugmentedSimplexCategory.equivAugmentedSimplicialObject
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
CategoryTheory.Functor AugmentedSimplexCategoryᵒᵖ C ≌ CategoryTheory.SimplicialObject.Augmented CThe equivalence between functors out of AugmentedSimplexCategory and augmented simplicial
objects.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 43 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.
Cites11
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 · cited by 8,081
- SimplexCategorystatement and proof · cited by 2,204
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.SimplicialObject.Augmentedstatement · cited by 113
- AugmentedSimplexCategorystatement · cited by 66
- CategoryTheory.Equivalence.transproof · cited by 57
- CategoryTheory.Equivalence.congrLeftproof · cited by 46
- CategoryTheory.WithTerminal.equivCommaproof · cited by 26
- CategoryTheory.WithInitial.opEquivproof · cited by 20
Cited by26
Results whose statement or proof uses this declaration.
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIsostatement and proof · cited by 4
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIsostatement and proof · cited by 2
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIsostatement and proof · cited by 2
- AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_appstatement · cited by 0
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_appstatement · cited by 0
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_appstatement · cited by 0
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_appstatement · cited by 0
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_appstatement · cited by 0