Rewriting modulo isotopies in pivotal linear (2,2)-categories

Benjamin Dupont 1
1 AGL - Algèbre, géométrie, logique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : In this paper, we study rewriting modulo a set of algebraic axioms in categories enriched in linear categories, called linear (2, 2)-categories. We introduce the structure of linear (3, 2)-polygraph modulo as a presentation of 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 for which we rewrite modulo. By this constructive method, we recover the bases of normally ordered dotted oriented Brauer diagrams in te affine oriented Brauer linear (2, 2)-category.
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Submitted on : Saturday, August 3, 2019 - 4:55:05 PM
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Benjamin Dupont. Rewriting modulo isotopies in pivotal linear (2,2)-categories. 2019. ⟨hal-02263268⟩



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