  Synthetic Differential Geometry (SDG) is a categorical version of
differential geometry based on enriching the real line with infinitesimals and
weakening of classical logic to intuitionistic logic. We show that SDG provides
an effective mathematical tool to formulate general relativity in
infinitesimally small domains. Such a domain is modelled by a monad around a
point $x$ of a manifold $M$, defined as a collection of points in $M$ that
differ from $x$ by an infinitesimal value. Monads have rich enough matematical
structure to allow for the existence of all geomeric quantities necesary to
construct general relativity "in the smallest". We focus on connection and
curvature. We also comment on the covariance principle and the equivalence
principle in this context. Identification of monads with what happens "beneath
the Planck threshold" could open new possibilities in our search for quantum
gravity theory.
