A category of quantum categories
Dimitri Chikhladze
TL;DR
This paper clarifies the structure of quantum categories, showing their relation to bialgebroids and defining functors and natural transformations within this framework, thus advancing the theoretical understanding of quantum algebraic structures.
Contribution
It provides detailed clarification of quantum categories, connecting them explicitly to bialgebroids and introducing notions of functor and natural transformation.
Findings
Explicit unpacking of quantum category axioms
Connection to bialgebroids in Hopf algebra literature
Definitions of functor and natural transformation for quantum categories
Abstract
Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set of axioms close to the definitions of a bialgebroid in the Hopf algebraic literature. We define notions of functor and natural transformation for quantum categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra