  The topological interpretation of modal logics provides descriptive languages
and proof systems for reasoning about points of topological spaces. Recent work
has been devoted to model checking of spatial logics on discrete spatial
structures, such as finite graphs and digital images, with applications in
various case studies including medical image analysis. These recent
developments required a generalisation step, from topological spaces to closure
spaces. In this work we initiate the study of bisimilarity and minimisation
algorithms that are consistent with the closure spaces semantics. For this
purpose we employ coalgebraic models. We present a coalgebraic definition of
bisimilarity for quasi-discrete models, which is adequate with respect to a
spatial logic with reachability operators, complemented by a free and
open-source minimisation tool for finite models. We also discuss the
non-quasi-discrete case, by providing a generalisation of the well-known
set-theoretical notion of topo-bisimilarity, and a categorical definition, in
the same spirit as the coalgebraic rendition of neighbourhood frames, but
employing the covariant power set functor, instead of the contravariant one. We
prove its adequacy with respect to infinitary modal logic.
