hasLimits_of_hasColimits_of_hasSeparator

English

If C is cocomplete, well-copowered and has a separator, then C is complete.

Русский

Если C кокономплетна, хорошо-конапowered и имеет сепаратор, то C полна пределами.

LaTeX

$$HasColimits C ∧ HasSeparator C ∧ WellPowered Cᵒᵖ ⇒ HasLimits C$$

Lean4

/-- A consequence of the special adjoint functor theorem: if `C` is complete, well-powered and
    has a separator, then it is complete. -/
theorem hasLimits_of_hasColimits_of_hasSeparator [HasColimits C] [HasSeparator C] [WellPowered.{v} Cᵒᵖ] : HasLimits C :=
  hasLimits_of_hasColimits_of_isSeparating <| isSeparator_separator C

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