Universal properties of Delannoy categories
Kevin Coulembier, Nate Harman, Andrew Snowden
Source abstract
Abstract Recently, Harman and Snowden introduced a new symmetric tensor category associated with an oligomorphic group with a measure . When 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 semisimple, 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 for a general oligomorphic group .
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