The Monoid of Inverse Maps

This report introduces the inverse map monoid. The monoid was found by exploring the space of all inverted maps. This monoid will build inverted maps which are bundles. The monoid is isomorphic to the monoid of maps. A number of morphisms of the inverse map monoid are introduced. 1 Introduction This report develops an algebraic structure, the monoid of inverse maps, which will be useful in the Irish School of Constructive Mathematics, see Mac an Airchinnigh [2, 3, 4]. In which algebraic structures and morphisms are used to specify and develop software systems. This algebraic structure is an example of the many algebraic structure which under pin computer systems. The finding of new algebraic structures also expands general mathematical knowledge, and so will useful to many of the current and future computer systems. Inverse maps are use in many specifications of software systems, such as consistently updating aliases in a system, see Mac an Airchinnigh [3, pages 43 -- 45], they are al...