Gauging noninvertible defects: a 2-categorical perspective

We generalize the notion of an anomaly for a symmetry to noninvertible enacted by surface operators using framework condensation in 2-categories. Given multifusion 2-category, potentially with some additional levels monoidality, we prove theorems about structure 2-category obtained condensing suitable algebra object. give examples where resulting category displays grouplike fusion rules and through cohomology computation, find obstruction further vacuum theory.