The connection between categorical and differential Galois theories established by the author (published in 1989) is extended to the context that includes difference Galois theory.
"Picard-Vessiot and categorically normal extensions in differential-difference Galois theory." Bull. Belg. Math. Soc. Simon Stevin 23 (5) 753 - 768, december 2016. https://doi.org/10.36045/bbms/1483671624