forkMap — Mathlib

English

An extended variant of the multiequalizer condition under HasMultiequalizer assumptions, yielding an equivalence of IsLimit structures between P and P ⋙ s.

Русский

Расширенный вариант условия мультиравенства под предпосылками HasMultiequalizer, дающий эквивалентность IsLimit между P и P ⋙ s.

LaTeX

$$$IsSheaf J P \\iff ∀ X,S, IsIso (S.toMultiequalizer P).$$$

Lean4

/-- The left morphism of the fork diagram given in Equation (3) of [MM92], as well as the fork
diagram of the Stacks entry. -/
@[stacks 00VM "The left morphism the fork diagram there."]
def forkMap : P.obj (op U) ⟶ firstObj R P :=
  Pi.lift fun f => P.map f.2.1.op

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