Association schemes, classical RCFT's, and centres of monoidal functor categories

Abstract

Here we describe three straightforward examples of what was called a graphic Fourier transformation in [4]. At least two of these examples may be viewed simply as monoidal comonads on suitable monoidal closed functor categories, but the third example, which involves "centres" of monoidal closed functor categories, is generally not comonadic. For the first two examples (i.e., association schemes and RCFT's), a more elaborate "probicategory" set-up was envisaged in an earlier version of this note, but many readers missed the main point so it is simplified (hopefully) below.