Keller sequences of exact $\infty$-categories

Abstract

We study a family of fibre-cofibre sequences in the $\infty$-category of exact $\infty$-categories, which we call Keller sequences, generalising the notion of Verdier sequences of stable $\infty$-categories. We show that algebraic K-theory is localising with respect to this family, and use this to give a categorical proof of Quillen's resolution theorem. Our arguments hinge upon a mapping space characterisation of special inclusions as studied by Keller, from which we deduce another proof of Keller's theorem that such inclusions induce fully faithful functors on stable envelopes.