Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Roe bimodules as morphisms of discrete metric spaces   For two discrete metric spaces, $X$ and $Y$ we consider metrics on $X\sqcup
Y$ compatible with the metrics on $X$ and $Y$. As morphisms from $X$ to $Y$ we
consider the Roe bimodules, i.e. the norm closures of bounded finite
propagation operators from $l^2(X)$ to $l^2(Y)$. We study the corresponding
category $\mathcal M$, which is also a 2-category. We show that almost
isometries determine morphisms in $\mathcal M$. We also consider the case
$Y=X$, when there is a richer algebraic structure on the set of morphisms of
$\mathcal M$: it is a partially ordered semigroup with the neutral element,
with involution, and with a lot of idempotents. We also give a condition when a
morphism is a $C^*$-algebra.

32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin