Categories of layered semirings
  We generalize the constructions of [17,19] to layered semirings, in order to enrich the structure and provide finite examples for applications in arithmetic (including finite examples). The layered category theory of [19] is extended accordingly, to cover noncancellative monoids. 
Zur Izhakian, Manfred Knebusch, Louis Rowen
math.RA math.CT