Computer-supported Exploration of a Categorical Axiomatization of Modeloids

Lucca Tiemens; Dana S. Scott; Christoph Benzmüller; Miroslav Benda

doi:10.1007/978-3-030-43520-2_19

paper

Computer-supported Exploration of a Categorical Axiomatization of Modeloids

arXiv:1910.12863 · doi:10.1007/978-3-030-43520-2_19

Abstract

A modeloid, a certain set of partial bijections, emerges from the idea to abstract from a structure to the set of its partial automorphisms. It comes with an operation, called the derivative, which is inspired by Ehrenfeucht-Fraïssé games. In this paper we develop a generalization of a modeloid first to an inverse semigroup and then to an inverse category using an axiomatic approach to category theory. We then show that this formulation enables a purely algebraic view on Ehrenfeucht-Fraïssé games.

24 pages; accepted for conference: Relational and Algebraic Methods in Computer Science (RAMICS 2020)