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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 C

The equivalence between functors out of AugmentedSimplexCategory and augmented simplicial objects.

Defined in
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic
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.

AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso · cited by 4AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso · cited by 2AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso · cited by 2AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_app · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_app · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_app · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_app · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app · cited by 0AugmentedSimplexCategory.…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategoryCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceCategoryTheory.SimplicialObject.Augmented · cited by 113SimplicialObject.AugmentedAugmentedSimplexCategory · cited by 66AugmentedSimplexCategoryCategoryTheory.Equivalence.trans · cited by 57Equivalence.transCategoryTheory.Equivalence.congrLeft · cited by 46Equivalence.congrLeftCategoryTheory.WithTerminal.equivComma · cited by 26WithTerminal.equivCommaCategoryTheory.WithInitial.opEquiv · cited by 20WithInitial.opEquivAugmentedSimplexCategory.equi…CITED BYCITES

Cites11

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Cited by26

Results whose statement or proof uses this declaration.