  Phase transitions in anyon models in (2+1)-dimensions can be driven by
condensation of bosonic particle sectors. We study such condensates in a
diagrammatic language and explicitly establish the relation between the states
in the fusion spaces of the theory with the condensate, to the states in the
parent theory using a new set of mathematical quantities called vertex lifting
coefficients (VLCs). These allow one to calculate the full set of topological
data ($S$-, $T$-, $R$- and $F$-matrices) in the condensed phase. We provide
closed form expressions of the topological data in terms of the VLCs and
provide a method by which one can calculate the VLCs for a wide class of
bosonic condensates. We furthermore furnish a concrete recipe to lift arbitrary
diagrams directly from the condensed phase to the original phase, such that
they can be evaluated using the data of the original theory and a limited
number of VLCs. Some representative examples are worked out in detail.
