  Finding all the mutually unbiased bases in various dimensions is a problem of
fundamental interest in quantum information theory and pure mathematics. The
general problem formulated in finite-dimensional Hilbert spaces is open. In the
categorical approach to quantum mechanics one can find examples of categories
which behave ``like'' the category of finite-dimensional Hilbert spaces in
various ways but are subtly different. One such category is the category of
sets and relations, $\mathbf{Rel}$. One can formulate the concept of mutually
unbiased bases here as well. In this note we classify all the mutually unbiased
bases in this category by relating it to a standard question in combinatorics.
