Keller sequences of exact categories

We introduce a family of fibre-cofibre sequences in the category of exact \(\infty\)-categories generalising the notion of Verdier sequences of stable \(\infty\)-categories, and study their \(K\)-theoretic behaviour: we show that connective algebraic \(K\)-theory is Keller localising, and use this to give a categorical proof of the Gillet-Waldhausen theorem. We also give a self-contained proof of Waldhausen’s additivity theorem for exact \(\infty\)-categories.