mk' — Mathlib

English

The naturality for σ₂ faces across i ∈ Fin 2 holds after mk.app, echoing the Segal-like coherence at level 1.

Русский

Натуральность для σ₂ лицевых отображений по i ∈ Fin 2 сохраняется после mk.app, отражая когерентность на уровне 1 подобно Segal.

LaTeX

$$$\forall i:\, Fin(2),\; toNerve₂.mk.naturalityProperty F (σ₂ i) $$$

Lean4

/-- An alternate version of `toNerve₂.mk`, which constructs a map of 2-truncated simplicial sets
`X ⟶ nerveFunctor₂.obj (Cat.of C)` from the underlying refl prefunctor under a composition
hypothesis, where that prefunctor the central hypothesis is conjugated by the isomorphism
`nerve₂Adj.NatIso.app C`. -/
@[simps!]
def mk' : X ⟶ nerveFunctor₂.obj (Cat.of C) :=
  toNerve₂.mk (F ≫ (OneTruncation₂.ofNerve₂.natIso.app (Cat.of C)).hom) hyp

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