{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {V : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} V] →
        [inst_2 : CategoryTheory.MonoidalCategory C] →
          [inst_3 : CategoryTheory.MonoidalCategory V] →
            {D : Type u₃} →
              [inst_4 : CategoryTheory.Category.{v₃, u₃} D] →
                (ι : CategoryTheory.Functor D (CategoryTheory.Functor C V)) →
                  ι.FullyFaithful →
                    [hasDayConvolution :
                        ∀ (d d' : D),
                          (CategoryTheory.MonoidalCategory.tensor C).HasPointwiseLeftKanExtension
                            (CategoryTheory.MonoidalCategory.externalProduct (ι.obj d) (ι.obj d'))] →
                      (∀ (d d' : D),
                          ι.essImage
                            ((CategoryTheory.MonoidalCategory.tensor C).pointwiseLeftKanExtension
                              (CategoryTheory.MonoidalCategory.externalProduct (ι.obj d) (ι.obj d')))) →
                        [hasDayConvolutionUnit :
                            (CategoryTheory.Functor.fromPUnit
                                  (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).HasPointwiseLeftKanExtension
                              (CategoryTheory.Functor.fromPUnit (CategoryTheory.MonoidalCategoryStruct.tensorUnit V))] →
                          ι.essImage
                              ((CategoryTheory.Functor.fromPUnit
                                    (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).pointwiseLeftKanExtension
                                (CategoryTheory.Functor.fromPUnit
                                  (CategoryTheory.MonoidalCategoryStruct.tensorUnit V))) →
                            CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore C V D