over_finiteProducts_of_finiteWidePullbacks

English

Given finite wide pullbacks in C, Over B has finite products.

Русский

Имея конечные широкие pullback в C, Over B имеет конечные произведения.

LaTeX

$$$[HasFiniteWidePullbacks C] \Rightarrow HasFiniteProducts(Over B)$$$

Lean4

/-- Given all finite wide pullbacks in `C`, construct finite products in `C/B`. -/
theorem over_finiteProducts_of_finiteWidePullbacks [HasFiniteWidePullbacks C] {B : C} : HasFiniteProducts (Over B) :=
  ⟨fun _ => over_product_of_widePullback⟩

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