Abstract
In this paper, we study linear rewriting systems modulo a set of algebraic axioms. We introduce the structure of linear (3,2)-polygraph modulo as a presentation of a category enriched in linear categories, (called a linear (2,2)-category), by a rewriting system modulo algebraic axioms. We introduce a symbolic computation method in order to compute linear bases for the vector spaces of 2-cells of these categories. In particular, we study the case of pivotal 2-categories using the isotopy relations given by biadjunctions on 1-cells and cyclicity conditions on 2-cells as axioms modulo. By this constructive method, we recover the bases of normally ordered dotted oriented Brauer diagrams in the affine oriented Brauer linear (2,2)-category.
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