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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02263268
Contributor : Benjamin Dupont <>
Submitted on : Saturday, August 3, 2019 - 4:55:05 PM
Last modification on : Tuesday, August 6, 2019 - 1:16:57 AM

File

rewrmodpiv.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02263268, version 1

Citation

Benjamin Dupont. Rewriting modulo isotopies in pivotal linear (2,2)-categories. 2019. ⟨hal-02263268⟩

Share

Metrics

Record views

23

Files downloads

14