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Picard-Vessiot rings are present in many settings like differential Galoistheory, difference Galois theory and Galois theory of Artinian simple modulealgebras. In this article we set up an abstract framework in which we can provetheorems on existence and uniqueness of Picard-Vessiot rings, as well as onGalois groups corresponding to the Picard-Vessiot rings. As the presentapproach restricts to the categorical properties which all the categories ofdifferential modules resp. difference modules etc. share, it gives unifiedproofs for all these Galois theories (and maybe more general ones).

A categorical approach to Picard-Vessiot theory