Categorical semigroups
Fred R. McMorris, M. Satyanarayana · Proceedings of the American Mathematical Society · 1972
The main purpose of this paper is to describe some properties of categorical semigroups, commutative semigroups which are categorical at zero, and determine the structure of commutative categorical semigroups. We also investigate whether Petrich’s tree condition, for categorical semigroups which are completely semisimple inverse semigroups, is necessary for arbitrary categorical semigroups.