Excision of skein categories and factorisation homology.

We prove that the skein categories of Walker–Johnson-Freyd satisfy excision. This allows us to conclude that skein categories are k -linear factorisation homology and taking the free cocompletion of skein categories recovers locally finitely presentable factorisation homology. An application of this is that the skein algebra of a punctured surface related to any quantum group with generic parameter gives a quantisation of the associated character variety. [ABSTRACT FROM AUTHOR]