instHasLimitsOfShapeOfHasCountableLimitsOfCountableCategory

English

If J is countable and C has countable limits, then HasLimitsOfShape J C holds for the countable category J.

Русский

Если J счётно и C имеет счётчые пределы, то HasLimitsOfShape J C выполняется для счётной категории J.

LaTeX

$$$[HasCountableLimits C] \\Rightarrow [HasLimitsOfShape J C]$ for countable J$$

Lean4

instance [HasCountableLimits C] [Category.{v} J] [CountableCategory J] : HasLimitsOfShape J C :=
  have : HasLimitsOfShape (HomAsType J) C := HasCountableLimits.out (HomAsType J)
  hasLimitsOfShape_of_equivalence (homAsTypeEquiv J)

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