We propose a categorification of the Chern character that refines earlier work of Toën and
Vezzosi and of Ganter and Kapranov. If X is an algebraic stack, our categorified Chern …

Making use of the theory of noncommutative motives, we characterize the topological
Dennis trace map as the unique multiplicative natural transformation from algebraic K-theory …

Traces in symmetric monoidal categories are well-known and have many applications; for
instance, their functoriality directly implies the Lefschetz fixed point theorem. However, for …

In this work we present a new approach to the theory of noncommutative motives and use it
to explain the different flavors of algebraic K-theory of schemes and dg-categories. The work …

In this article we further the study of non-commutative motives, initiated in [12, 43]. Our main
result is the construction of a symmetric monoidal structure on the localizing motivator …

In this paper, we present an infinity-categorical version of the theory of monoidal categories.
We show that the infinity category of spectra admits an essentially unique monoidal structure …

We organize the modified trace theory with the use of the Nakayama functor of finite abelian
categories. For a linear right exact functor Σ on a finite abelian category MM, we introduce …

Let $\V $ be a symmetric monoidal model category and let $ X $ be an object in $\V $. From
this we can construct a new symmetric monoidal model category $ Sp^{\Sigma}(\V, X) $ of …

We define analogues of homogeneous coordinate algebras for noncommutative two-tori
with real multiplication. We prove that the categories of standard holomorphic vector bundles …

We describe a general framework for notions of commutativity based on enriched category
theory. We extend Eilenberg and Kelly's tensor product for categories enriched over a …