  We prove the second adjointness in the setting of the categorical local
Langlands correspondence. Moreover, we study the relation between Eisenstein
series and cuspidal supports and present a conjectural characterization of
irreducible smooth representations with supercuspidal $L$-parameters regarding
geometric constant terms. The main technical ingredient is an induction
principle for geometric Eisenstein series which allows us to reduce to the
situations already treated in the literature.
