nerveFunctor₂ — Mathlib

English

There is a natural isomorphism between nerveFunctor and nerveFunctor₂ composed with Truncated.cosk 2.

Русский

Существует естественная изоморфизм между nerveFunctor и nerveFunctor₂, композиции с Truncated.cosk 2.

LaTeX

$$$ \text{cosk}_2\text{Iso} : \mathrm{nerve\,Functor} \cong \mathrm{nerve\,Functor}_2 \circ \mathrm{Truncated.cosk}(2) $$$

Lean4

/-- The essential data of the nerve functor is contained in the 2-truncation, which is
recorded by the composite functor `nerveFunctor₂`. -/
def nerveFunctor₂ : Cat.{v, u} ⥤ SSet.Truncated 2 :=
  nerveFunctor ⋙ truncation 2

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