We propose a topological paradigm in alterfold topological quantum field theory to explore various concepts, including modular invariants, \(\alpha \) -induction and connections in Morita contexts within a modular fusion category of non-zero global dimension over an arbitrary field. Using our topological perspective, we provide streamlined quick proofs and broad generalizations of a wide range of results. These include all theoretical findings by Böckenhauer, Evans, and Kawahigashi on \(\alpha \) -induction. Additionally, we introduce the concept of double \(\alpha \) -induction for pairs of Morita contexts and define its higher-genus Z-transformation, which remains invariant under the action of the mapping class group. Finally, we establish a novel integral identity for modular invariants across multiple Morita contexts, unifying several known identities as special cases.
