hasSmallLocalizedShiftedHom_iff_target

English

If a morphism f: Y → Y' is W-equivalent, then HasSmallLocalizedShiftedHom W M X Y is equivalent to HasSmallLocalizedShiftedHom W M X Y'.

Русский

Если мехизм f: Y → Y' эквивалентен по W, то HasSmallLocalizedShiftedHom W M X Y эквивалентно HasSmallLocalizedShiftedHom W M X Y'.

LaTeX

$$$ HasSmallLocalizedShiftedHom^{w} W M X Y \iff HasSmallLocalizedShiftedHom^{w} W M X Y' $$$

Lean4

theorem hasSmallLocalizedShiftedHom_iff_target [W.IsCompatibleWithShift M] {Y' : C} (f : Y ⟶ Y') (hf : W f) :
    HasSmallLocalizedShiftedHom.{w} W M X Y ↔ HasSmallLocalizedShiftedHom.{w} W M X Y' :=
  forall_congr' (fun a ↦ forall_congr' (fun b ↦ hasSmallLocalizedHom_iff_target W (X⟦a⟧) (f⟦b⟧') (W.shift hf b)))

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