  The Long-Moody construction is a method to obtain representations of braid
groups introduced by Long and Moody. Also the Katz middle convolution is known
to be a method to construct local systems on
$\mathbb{C}\backslash\{n\text{-points}\}$ introduced by Katz. In this paper, we
explain that these two methods are naturally unified and define a new functor
which we call the Katz-Long-Moody functor. This functor extends the framework
of Katz algorithm to categories of local systems on various topological spaces,
for example, $B_{n}$-bundles associated with simple Weierstrass polynomials,
complements of hyperplane arrangements of fiber-type, link complements in the
solid torus, and so on.
