Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cross-connections of linear transformation semigroup   Cross-connection theory developed by Nambooripad is the construction of a
semigroup from its principal left (right) ideals using categories. We briefly
describe the general cross-connection theory for regular semigroups and use it
to study the {normal categories} arising from the semigroup $Sing(V)$ of
singular linear transformations on an arbitrary vectorspace $V$ over a field
$K$. There is an inbuilt notion of duality in the cross-connection theory, and
we observe that it coincides with the conventional algebraic duality of vector
spaces. We describe various cross-connections between these categories and show
that although there are many cross-connections, upto isomorphism, we have only
one semigroup arising from these categories. But if we restrict the categories
suitably, we can construct some interesting subsemigroups of the {variant} of
the linear transformation semigroup.

28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int