Reconstruction Theory

Abstract

Suppose that G is a compact group. Denote by \underline{Rep} G the category whose objects are the continuous finite dimensional unitary representations of G and whose morphisms are the intertwining operators--then \underline{Rep} G is a monoidal *-category with certain properties P_1,P_2, ... . Conversely, if \underline{C} is a monoidal *-category possessing properties P_1,P_2, ..., can one find a compact group G, unique up to isomorphism, such that \underline{Rep} G "is" \underline{C}? The central conclusion of reconstruction theory is that the answer is affirmative.