Constructions in the category of real semigroups
Max A. Dickmann, Francisco Miraglia, Alejandro Petrovich · Contemporary mathematics - American Mathematical Society · 2017
The purpose of this research paper is threefold: first, to introduce new constructions in the category of real semigroups (RS): locally constant functions on a topological space with values in a RS, directed inductive limits and RS-sums, an analog of a coproduct for RSs. Secondly, to obtain some understanding of the space of RS-characters of an infinite product of RSs and, lastly, to establish the preservation of finite products and arbitrary directed inductive limits by the natural functor from the category of commutative unitary rings into that of RSs. The basic references for real semigroups, whose notation and terminology we adopt, are the papers cited under Dickmann-Petrovich (see References). We are grateful to the referee for the careful reading of the text and the valuable comments and corrections that improved the presentation.