  Transformational music theory mainly deals with group and group actions on
sets, which are usually constituted by chords. For example, neo-Riemannian
theory uses the dihedral group D24 to study transformations between major and
minor triads, the building blocks of classical and romantic harmony. Since the
developments of neo-Riemannian theory, many developments and generalizations
have been proposed, based on other sets of chords, other groups, etc. However
music theory also face problems for example when defining transformations
between chords of different cardinalities, or for transformations that are not
necessarily invertible. This paper introduces a categorical construction of
musical transformations based on category extensions using groupoids. This can
be seen as a generalization of a previous work which aimed at building
generalized neo-Riemannian groups of transformations based on group extensions.
The categorical extension construction allows the definition of partial
transformations between different set-classes. Moreover, it can be shown that
the typical wreath products groups of transformations can be recovered from the
category extensions by "packaging" operators and considering their composition.
