  In this article we study the possible Morita equivalence classes of algebras
in three families of fusion categories (pointed, near-group and $A \left( 1,l
\right)_{\frac{1}{2}}$) by studying the Non-negative Integer Matrix
representations (NIM-reps) of their underlying fusion ring, and compare these
results with existing classification results of algebra objects. Also, in an
appendix we include a test of the exponents conjecture for modular tensor
categories of rank up to 4.
