Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravity in the smallest   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.

21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin