Incidence category of the Young lattice, injections between finite sets, and Koszulity
(English)Article in journal (Other academic) Submitted
We study the quadratic quotients of the incidence category of the Young lattice defined using the zero relations corresponding to adding two boxes to the same row, or to the same column or both. We show that the latter quotient corresponds to the Koszul dual of the original incidence category while the first two quotients are, in a natural way, Koszul duals of each other, hence they are in particular Koszul self-dual. Both of these two quotients are known to be basic representatives in the Morita equivalence class of the category of injections between finite sets. We also present a new, rather direct, argument establishing this Morita equivalence.
Algebra and Logic
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-303704OAI: oai:DiVA.org:uu-303704DiVA: diva2:972825