hasLimitsOfShape_of_isConnected — Mathlib

English

Similarly, the snd projection interacts with the pullback via the left iso; the composition equals the snd projection of the product’s left component.

Русский

Аналогично: правая проекция через левый изоморфизм через связь с произведением совпадает с проекцией snd.

LaTeX

$$$$ (\mathrm{prodLeftIsoPullback}\, Y\, Z)^{\mathrm{hom}} \circ \mathrm{pullback.snd}\; (Y.hom, Z.hom) = \mathrm{prod.snd}_{X:=Y}.\mathrm{left} $$$$

Lean4

/-- The over category has any connected limit which the original category has. -/
instance hasLimitsOfShape_of_isConnected {B : D} [IsConnected J] [HasLimitsOfShape J C] :
    HasLimitsOfShape J (CostructuredArrow K B) where has_limit F := hasLimit_of_created F (CostructuredArrow.proj K B)

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