Introducci\'on a la teor\'ia de categor\'ias, l\'ogica y topos elementales para una mente curiosa

TL;DR

This paper introduces elementary topos theory and categorical logic in an accessible way, illustrating how categories can lead to non-classical logical systems with multiple truth values, aimed at a broader audience.

Contribution

It simplifies the concepts of category theory and topos logic for non-specialists, demonstrating their relevance to alternative logical systems.

Findings

Elementary topos of graphs has three additional truth values.

Accessible explanation of categorical logic for non-mathematicians.

Illustration of non-classical logic arising from topos theory.

Abstract

This paper presents a study of how the theory of categories leads to the creation of non classical logical systems. In particular, the case of the elementary topos of graphs, where there are three other truth values different from false and true. The approach in this article to the theory of categories avoids specialized mathematical training to understand it, since it seeks to make accessible the main ideas of this branch of mathematics to other disciplines of knowledge. This work was presented by the second author, under the title of "Logic and Categories", at the I Colloquium on Logic, Epistemology and Methodology organized by the School of Philosophy of the University sity of Costa Rica.