Rewriting in Gray categories with applications to coherence

Abstract Over the recent years, theory of rewriting has been used and extended in order to provide systematic techniques show coherence results for strict higher categories. Here, we investigate a further generalization Gray categories, which are known be equivalent tricategories. This requires us develop setting precategories, adapted mechanized computations include categories as particular cases. We that finite system precategories admits number critical pairs, can efficiently computed. also extend Squier’s theorem our context, showing convergent is coherent, means any two parallel 3-cells necessarily equal. allows prove several well-known structures context categories: monoids, adjunctions, Frobenius monoids.