equivAugmentedCosimplicialObjectFunctorCompToArrowIso

English

There is a natural isomorphism between the composed functors AugmentedCosimplicialObject and the evaluation at a canonical arrow in C.

Русский

Существует естественное изоморфизм между композицией AugmentedCosimplicialObject и оценкой по каноническому стрелу в C.

LaTeX

$$EquivAugmentedCosimplicialObjectFunctorCompToArrowIso$$

Lean4

/-- Through the equivalence `(AugmentedSimplexCategory ⥤ C) ≌ CosimplicialObject.Augmented C`,
the arrow attached to the cosimplicial object is the one obtained by evaluation at the unique arrow
`star ⟶ of [0]`. -/
@[simps!]
def equivAugmentedCosimplicialObjectFunctorCompToArrowIso :
    equivAugmentedCosimplicialObject.functor ⋙ CosimplicialObject.Augmented.toArrow ≅
      Functor.mapArrowFunctor _ C ⋙ (evaluation _ _ |>.obj <| .mk <| WithInitial.homTo <| .mk 0) :=
  .refl _

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