Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum geometry of Boolean algebras and de Morgan duality   We take a fresh look at the geometrization of logic using the recently
developed tools of `quantum Riemannian geometry' applied in the digital case
over the field $\Bbb F_2=\{0,1\}$, extending de Morgan duality to this context
of differential forms and connections. The 1-forms correspond to graphs and the
exterior derivative of a subset amounts to the arrows that cross between the
set and its complement. The line graph $0-1-2$ has a non-flat but Ricci flat
quantum Riemannian geometry. The previously known four quantum geometries on
the triangle graph, of which one is curved, are revisited in terms of
left-invariant differentials, as are the quantum geometries on the dual Hopf
algebra, the group algebra of $\Bbb Z_3$. For the square, we find a moduli of
four quantum Riemannian geometries, all flat, while for an $n$-gon with $n>4$
we find a unique one, again flat. We also propose an extension of de Morgan
duality to general algebras and differentials over $\Bbb F_2$.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
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The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph