  The famous biologist Robert Rosen argued for an intrinsic difference between
biological and artificial life, supporting the claim that `living systems are
not mechanisms'. This result, understood as the claim that life-like mechanisms
are non-computable, can be phrased as the non-existence of an equivalence
between a category of `static'/analytic elements and a category of
`variable'/synthetic elements.
  The property of a system of being synthetic, understood as being the gluing
of `variable families' of analytica, must imply that the latter class of
objects does not retain sufficient information in order to describe said
variability; we contribute to this thesis with an argument rooted in elementary
category theory.
  Seen as such, Rosen's `proof' that no living system can be a mechanism arises
from a tension between two contrapuntal needs: on one side, the necessity to
consider (synthetically) variable families of systems; on the other, the
necessity to describe a syntheticum via an universally chosen analyticum.
