arXiv:math/0601185v5 [math.KT] 19 Jun 2006 Page 1 arXiv:math/0601185v5 [math.KT] 19 Jun
2006 ON DIFFERENTIAL GRADED CATEGORIES BERNHARD KELLER Abstract. Differential …

In this paper we establish a universal characterization of higher algebraic K–theory in the
setting of small stable∞–categories. Specifically, we prove that connective algebraic K …

We prove the conjecture that any Grothendieck $(\infty, 1) $-topos can be presented by a
Quillen model category that interprets homotopy type theory with strict univalent universes …

A stable model category is a setting for homotopy theory where the suspension functor is
invertible. The prototypical examples are the category of spectra in the sense of stable …

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 …

This purpose of this book is twofold: to provide a general introduction to higher category
theory (using the formalism of" quasicategories" or" weak Kan complexes"), and to apply this …

We realise Joyal'cell category Θ as a dense subcategory of the category of ω-categories.
The associated cellular nerve of an ω-category extends the well-known simplicial nerve of a …

We define a derived version of Mazur's Galois deformation ring. It is a pro-simplicial ring R
classifying deformations of a fixed Galois representation to simplicial coefficient rings; its …

We introduce the dendroidal analogues of the notions of complete Segal space and of Segal
category, and construct two appropriate model categories for which each of these notions …

In this paper we re-develop the foundations of the category theory of quasi-categories (also
called∞-categories) using 2-category theory. We show that Joyal's strict 2-category of quasi …