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 …

Equivariant homotopy theory started from geometrically motivated questions about
symmetries of manifolds. Several important equivariant phenomena occur not just for a …

We establish a canonical and unique tensor product for commutative monoids and groups in
an∞–category C which generalizes the ordinary tensor product of abelian groups. Using …

We provide general conditions under which the algebras for a coloured operad in a
monoidal model category carry a Quillen model structure, and prove a Comparison Theorem …

The connective topological modular forms spectrum, $ tmf $, is in a sense initial among
elliptic spectra, and as such is an important link between the homotopy groups of spheres …

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

Category theory provides structure for the mathematical world and is seen everywhere in
modern mathematics. With this book, the author bridges the gap between pure category …

The homotopy theory of∞‐operads is defined by extending Joyal's homotopy theory of∞‐
categories to the category of dendroidal sets. We prove that the category of dendroidal sets …

Notions of generalized multicategory have been defined in numerous contexts throughout
the literature, and include such diverse examples as symmetric multicategories, globular …

We provide a very general approach to placing model structures and semi-model structures
on algebras over symmetric colored operads. Our results require minimal hypotheses on the …