2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/183309A Morita class of symmetric special Frobenius algebras A in the modular tensor category of a chiral CFT determines a full CFT on oriented world sheets. For unoriented world sheets, A must in addition possess a reversion, i.e. an isomorphism from A^opp to A squaring to the twist. Any two reversions of an algebra A differ by an element of the group Aut(A) of algebra automorphisms of A. We establish a group homomorphism from Aut(A) to the Picard group of the bimodule category C_AA, with kernel consisting of the inner automorphisms, and we refine Morita equivalence to an equivalence relation between algebras with reversion.22 pagesCategory TheoryHigh Energy Physics - TheoryMathematical PhysicsQuantum Algebra81T40,18D10,18D35,81T45text