Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedding convex geometries and a bound on convex dimension   The notion of an abstract convex geometry offers an abstraction of the
standard notion of convexity in a linear space. Kashiwabara, Nakamura and
Okamoto introduce the notion of a generalized convex shelling into $\mathbb{R}$
and prove that a convex geometry may always be represented with such a
shelling. We provide a new, shorter proof of their result using a recent
representation theorem of Richter and Rubinstein, and deduce a different upper
bound on the dimension of the shelling.

12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga