instMonoActionFintypeCatImageComplementIncl

English

The inclusion map from the image complement into Y is mono in the category of finite G-sets.

Русский

Включение дополнения образа в Y моно в категории конечных G-наборов.

LaTeX

$$$\\text{imageComplementIncl } G f: \\mathrm{imageComplement } G f \\hookrightarrow Y\\text{ is mono}$$$

Lean4

instance {X Y : Action FintypeCat G} (f : X ⟶ Y) : Mono (Action.imageComplementIncl G f) :=
  by
  apply Functor.mono_of_mono_map (forget _)
  apply ConcreteCategory.mono_of_injective
  exact Subtype.val_injective

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