2025/10/11 by Coulembier, Kevin, Harman, Nate, Snowden, Andrew · 1 citation
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2510.10317
Recently, the second and third authors introduced a new symmetric tensor category \underlinePerm(G, μ) associated to an oligomorphic group G with a measure μ. When G is the group of order preserving self-bijections of the real line there are four such measures, and the resulting tensor categories are called the Delannoy categories. The first Delannoy category is semi-simple, and was studied in detail by Harman, Snowden, and Snyder. We give universal properties for all four Delannoy categories in terms of ordered étale algebras. As a consequence, we show that the second and third Delannoy categories admit at least two local abelian envelopes, and the fourth admits at least four. We also prove a coarser universal property for \underlinePerm(G, μ) for a general oligomorphic group G.