  In this paper, we introduce a rewriting theory of linear monoidal categories.
Those categories are a particular case of what we will define as linear (n,
p)-categories. We will also define linear (n, p)-polygraphs, a linear adapation
of n-polygraphs, to present linear (n -- 1, p)-categories. We focus then on
linear (3, 2)-polygraphs to give presentations of linear monoidal categories.
We finally give an application of this theory in linear (3, 2)-polygraphs to
prove a basis theorem on the category AOB with a new method using a rewriting
property defined by van Ostroom: decreasingness.
