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Theorems · Definition · category theory

AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    AugmentedSimplexCategory.equivAugmentedCosimplicialObject.functor.comp
        CategoryTheory.CosimplicialObject.Augmented.drop ≅
      (CategoryTheory.Functor.whiskeringLeft SimplexCategory AugmentedSimplexCategory C).obj
        AugmentedSimplexCategory.inclusion

Through the equivalence (AugmentedSimplexCategory ⥤ C) ≌ CosimplicialObject.Augmented C, dropping the augmentation corresponds to precomposition with inclusion : SimplexCategory ⥤ AugmentedSimplexCategory.

Defined in
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic
Cited by
2 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_hom_app_app · cited by 0AugmentedSimplexCategory.…AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_inv_app_app · cited by 0AugmentedSimplexCategory.…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Iso · cited by 3963CategoryTheory.IsoSimplexCategory · cited by 2204SimplexCategoryCategoryTheory.Equivalence.functor · cited by 1268Equivalence.functorCategoryTheory.Iso.refl · cited by 727Iso.reflCategoryTheory.Functor.whiskeringLeft · cited by 395Functor.whiskeringLeftCategoryTheory.CosimplicialObject · cited by 125CategoryTheory.Cosimplici…CategoryTheory.CosimplicialObject.Augmented · cited by 72CosimplicialObject.Augmen…AugmentedSimplexCategory · cited by 66AugmentedSimplexCategoryAugmentedSimplexCategory.equivAugmentedCosimplicialObject · cited by 23AugmentedSimplexCategory.…CategoryTheory.CosimplicialObject.Augmented.drop · cited by 7Augmented.dropAugmentedSimplexCategory.inclusion · cited by 6AugmentedSimplexCategory.…AugmentedSimplexCategory.equi…CITED BYCITES

Cites15

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Cited by2

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