A coherence theorem for pseudonatural transformations

Maxime Lucas (1, 2)

1 PI.R2 - Design, study and implementation of languages for proofs and programs
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

We prove coherence theorems for bicategories, pseudofunctors and pseudonatural transformations. These theorems boil down to proving the coherence of some free $(4,2)$-categories. In the case of bicategories and pseudofunctors, existing rewriting techniques based on Squier's Theorem allow us to conclude. In the case of pseudonatural transformations this approach only proves the coherence of part of the structure, and we use a new rewriting result to conclude. To this end, we introduce the notions of white-categories and partial coherence.

Domaines: Catégories et ensembles [math.CT]

Maxime Lucas. A coherence theorem for pseudonatural transformations. Journal of Pure and Applied Algebra, 2017, 221 (5), pp.1146-1217. ⟨10.1016/j.jpaa.2016.09.005⟩. ⟨hal-01191867v2⟩