  We consider the fully parabolic, spatially heterogeneous chemotaxis-growth
system \begin{align*}
  \begin{cases}
  u_t = \Delta u - \nabla\cdot(u\nabla v) + \kappa(x)u-\mu(x)u^2, \\
  v_t = \Delta v - v + u
  \end{cases} \end{align*} in bounded domains $\Omega\subset \mathbb{R}^2$ and
show that the blow-up set is contained in the set of zeroes of $\mu$.
