Abstract: By work of Almkvist and Campbell, for a commutative ring R, the ring of big Witt vectors on R, W(R), is a completion of the Grothendieck ring of the category of endomorphisms of finitely generated projectives over R. On the other hand, the usual operations on Witt vectors, like Verschiebung and Frobenius can be defined at a categorical level. We extend the categorical operations of Verschiebung and Frobenius to the case where R is a non-commutative ring and show that these satisfy some expected properties. We also show that these play well with the iterated traces of endomorphisms, or ghost maps. Our work is inspired by the definition of Witt vectors in the non-commutative setting by Dotto, Krause, Nikolaus, and Patchkoria. This is Joint work with Agarwal, Campbell, Ponto, and Sun.