Computer-supported Exploration of a Categorical Axiomatization of Modeloids
Logic in Computer Science
2022-12-12 v2 Algebraic Topology
Category Theory
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-Fra\"iss\'e 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-Fra\"iss\'e games.
Keywords
Cite
@article{arxiv.1910.12863,
title = {Computer-supported Exploration of a Categorical Axiomatization of Modeloids},
author = {Lucca Tiemens and Dana S. Scott and Christoph Benzmüller and Miroslav Benda},
journal= {arXiv preprint arXiv:1910.12863},
year = {2022}
}
Comments
24 pages; accepted for conference: Relational and Algebraic Methods in Computer Science (RAMICS 2020)