isLimitOfPreserves₂ — Mathlib

English

There is an isomorphism between the colimit of the uncurry construction and the external product of the G-applied colimits.

Русский

Существующий изоморфизм между колимитом uncurry и внешним произведением колимитов, применённых к G.

LaTeX

$$$\\mathrm{colimit}(\\text{uncurry}(\\cdots)) \\cong (G(\\mathrm{colimit}K1)).(\\mathrm{colimit}K2)$$$

Lean4

/-- If `PreservesLimit₂ K₁ K₂ G`, obtain that `G.mapCone₂ c₁ c₂` is a limit cone
whenever c₁ c₂ are limit cones. -/
noncomputable def isLimitOfPreserves₂ [PreservesLimit₂ K₁ K₂ G] {c₁ : Cone K₁} (hc₁ : IsLimit c₁) {c₂ : Cone K₂}
    (hc₂ : IsLimit c₂) : IsLimit (G.mapCone₂ c₁ c₂) :=
  PreservesLimit₂.nonempty_isLimit_mapCone₂ hc₁ hc₂ |>.some

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