Introduction to Category Theory, Logic, and Elementary Topoi for a Curious Mind

Abstract

This paper presents a study of how the theory of categories leads to the creation ofnon-classical logical systems. In particular, the case of the elementary topos of graphs, wherethere are three other truth values different from false and true. The approach in this article tothe theory of categories avoids specialized mathematical training to understand it, since itseeks to make accessible the main ideas of this branch of mathematics to otherdisciplines ofknowledge. This work was presented by the second author, under the title of«Logic andCategories», at the I Colloquium on Logic, Epistemology and Methodology organized by theSchool of Philosophy of the University of Costa Rica.