initiallySmall_of_initial_of_initiallySmall

English

If F : K ⥤ J is initial and K is InitiallySmall, then J is InitiallySmall.

Русский

Если F : K ⥤ J начальный и K JustinlySmall, то J является InitiallySmall.

LaTeX

$$$[Initial\\;F] \\land [InitiallySmall\\;K] \\Rightarrow [InitiallySmall\\;J]$$$

Lean4

theorem initiallySmall_of_initial_of_initiallySmall [InitiallySmall.{w} K] (F : K ⥤ J) [Initial F] :
    InitiallySmall.{w} J :=
  suffices Initial ((fromInitialModel K) ⋙ F) from .mk' ((fromInitialModel K) ⋙ F)
  initial_comp _ _

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