vPullbackConeIsLimit — Mathlib

English

The descent morphism desc F s satisfies the universal property with respect to the cocone F, giving the factorization through the cocone.

Русский

Desc F s удовлетворяет универсальному свойству по отношению к коскопу F, обеспечивая факторизацию через него.

LaTeX

$$$\text{desc}_F^s: s.pt.presheaf.obj U \to \text{colimit.desc} (F \ colimit) ...$$$

Lean4

/-- The following diagram is a pullback, i.e. `Vᵢⱼ` is the intersection of `Uᵢ` and `Uⱼ` in `X`.

Vᵢⱼ ⟶ Uᵢ
 |      |
 ↓      ↓
 Uⱼ ⟶ X
-/
def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
  𝖣.vPullbackConeIsLimitOfMap forgetToPresheafedSpace i j (D.toPresheafedSpaceGlueData.vPullbackConeIsLimit _ _)

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