instHasColimitProd — Mathlib

English

A higher-order compatibility condition holds between the projections of the limit cones and the curry-lim structure.

Русский

Сохраняется условие совместимости между проекциями предельных конусов и структурой curry-lim.

LaTeX

$$$\text{IsLimit}(\text{coneOfHasLimitCurryCompLim } G) \Rightarrow \text{compatibility}(\text{lim},\text{curry})$$$

Lean4

/-- The functor `G` has a colimit if `C` has `K`-shaped colimits and `(curry.obj G ⋙ colim)` has a
colimit. -/
instance : HasColimit G where
  exists_colimit :=
    ⟨{  cocone := coconeOfHasColimitCurryCompColim G
        isColimit := isColimitCoconeOfHasColimitCurryCompColim G }⟩

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