We verify the existence of left Bouseld localizations and of enriched left Bouseld localizations, and we prove a collection of useful technical results characterizing certain brations of (enriched)… Expand

We prove that Waldhausen K ‐theory, when extended to a very general class of quasicategories, can be described as a Goodwillie differential. In particular, K ‐theory spaces admit canonical… Expand

We axiomatise the theory of $(\infty,n)$-categories. We prove that the space of theories of $(\infty,n)$-categories is a $B(\mathbb{Z}/2)^n$. We prove that Rezk's complete Segal $\Theta_n$-spaces,… Expand

We prove that the K-theory of an exact quasicategory can be computed via a higher categorical variant of the Q construction. This construction yields a quasicategory whose weak homotopy type is a… Expand

In this paper we introduce the notion of an operator category and two different models for homotopy theory of $\infty$-operads over an operator category -- one of which extends Lurie's theory of… Expand

The new homotopy theory of exact$\infty$-categories is introduced and employed to prove a Theorem of the Heart for algebraic $K$-theory (in the sense of Waldhausen). This implies a new compatibility… Expand

The new homotopy theory of exact ∞ - categories is introduced and employed to prove a Theorem of the Heart for algebraic K -theory (in the sense of Waldhausen). This implies a new compatibility… Expand