REWRITING IN HIGHER DIMENSIONAL LINEAR CATEGORIES AND APPLICATION TO THE AFFINE ORIENTED BRAUER CATEGORY

Clément Alleaume (1)

1 AGL - Algèbre, géométrie, logique

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.

Domaines: Théorie des représentations [math.RT]; Catégories et ensembles [math.CT]

Clément Alleaume. REWRITING IN HIGHER DIMENSIONAL LINEAR CATEGORIES AND APPLICATION TO THE AFFINE ORIENTED BRAUER CATEGORY. 2016. ⟨hal-01281219⟩