instPreservesColimitsOfShapeFintypeCatSingleObjOfFinite

English

A fiber functor reflects colimits of shapeDiscrete PEmpty.

Русский

Фибровый функтор отражает колимиты формы Discrete PEmpty.

LaTeX

$$$\\mathrm{ReflectsColimitsOfShape}(\\mathrm{Discrete}~\\mathrm{PEmpty})\\ F$$$

Lean4

/-- Fiber functors preserve quotients by finite groups in arbitrary universes. -/
instance {G : Type*} [Group G] [Finite G] : PreservesColimitsOfShape (SingleObj G) F :=
  by
  choose G' hg hf he using Finite.exists_type_univ_nonempty_mulEquiv G
  exact Limits.preservesColimitsOfShape_of_equiv he.some.toSingleObjEquiv.symm F

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