A Categorical Approach to the Study of Non-Commutative Motives

Abstract

We introduce a novel categorical framework for the study of non-commutative motives, drawing connections between derived categories of non-commutative spaces and classical motives in algebraic geometry. By leveraging advancements in ho-mological algebra and category theory, we develop tools to analyze and classify non-commutative algebraic structures through their associated motives. Our ap-proach provides new insights into the structure of non-commutative spaces and establishes a foundation for further exploration in both algebraic geometry and non-commutative geometry.