  We describe a categorical approach to finite noncommutative geometries.
Objects in the category are spectral triples, rather than unitary equivalence
classes as in other approaches. This enables to treat fluctuations of the
metric and unitary equivalences on the same footing, as representatives of
particular morphisms in this category. We then show how a matrix geometry
(Moyal plane) emerges as a fluctuation from one point, and discuss some
geometric aspects of this space.
