Quantum semigroup structures on quantum families of maps

TL;DR

This paper explores the theory of quantum families of maps, focusing on the emergence of quantum semigroup structures within this framework, providing foundational insights into their mathematical properties.

Contribution

It offers a detailed exposition of quantum semigroup structures in the context of quantum families of maps, advancing understanding of their algebraic and analytical features.

Findings

Quantum semigroup structures are naturally associated with quantum families of maps.

The paper clarifies the mathematical framework underpinning these structures.

Foundational results on the properties of quantum semigroups in this setting.

Abstract

These are notes accompanying lectures at 7th ILJU School of Mathematics "Banach Spaces and Related Topics" in Gyeongju, Koera. The lectures are devoted to exposition of the theory of quantum families of maps with emphasis on the study of quantum semigroup structures appearing in this context.