Skein Categories

Explore skein categories, a categorical analogue of skein algebras based on coloured ribbon tangles, in this comprehensive lecture. Delve into the concept of excision and how skein categories fit within the framework of factorisation homology as k-linear factorisation homology theories of surfaces. Examine the relationship between skein categories, Alekseev's moduli algebras, and stated skein algebras. Cover topics such as coloured ribbon graphs, the category of coloured ribbons, evaluation functions, relative tensor products, and characterisation. Investigate the Temperly-Lieb category and reflection equation algebras, providing a thorough understanding of this complex mathematical subject.

Introduction
Coloured Ribbon Graphs
Category of Coloured Ribbons
Evaluation Function
Skein Category (Walker, Johnson-Freyd)
Relative Tensor Product
Characterisation
Skein Categories as Factorisation Homology
Stated Skein Algebras (Le)
Temperly-Lieb Category
Reflection Equation Algebras (Majid)
Alekseev Moduli Algebra