fork — Mathlib

English

The ith component of res ≫ limit.π over Discrete functor equals F.map(leSupr i).op.

Русский

i-ая компонента рез ≫ limit.π равна F.map(leSupr i).op.

LaTeX

$$$\text{Eq }(\mathrm{res} F U,\ \lim_\pi)_{i} = F(\mathrm{leSupr}(U,i)).op$$$

Lean4

/-- The restriction map `F.obj U ⟶ Π F.obj (U i)` gives a cone over the equalizer diagram
for the sheaf condition. The sheaf condition asserts this cone is a limit cone.
-/
def fork : Fork.{v} (leftRes F U) (rightRes F U) :=
  Fork.ofι _ (w F U)

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