Graduate students and researchers alike will benefit from this treatment of classical and
modern topics in homotopy theory of topological spaces with an emphasis on cubical …

Working in the context of symmetric spectra, we consider algebraic structures that can be
described as algebras over an operad O. Topological Quillen homology, or TQ-homology, is …

We construct a Goodwillie tower of categories which interpolates between the category of
pointed spaces and the category of spectra. This tower of categories refines the Goodwillie …

Goodwillie calculus is a method for analyzing functors that arise in topology. One may think
of this theory as a categorification of the classical differential calculus of Newton and …

We develop a theory of Mackey functors on epiorbital categories which simultaneously
generalizes the theory of genuine $ G $-spectra for a finite group $ G $ and the theory of $ n …

Given an adjunction F⊣ G connecting reasonable categories with weak equivalences, we
define a new derived bar and cobar construction associated to the adjunction. This yields …

This introduction to higher category theory is intended to a give the reader an intuition for
what (∞, 1)-categories are, when they are an appropriate tool, how they fit into the …

We show that Koszul duality for operads in (Top,×) (Top,*) can be expressed via generalized
Thom complexes. As an application, we prove the Koszul self‐duality of the right module EM …

We give a survey of a generalization of Quillen–Sullivan rational homotopy theory which
gives spectral algebra models of unstable v_n-periodic homotopy types. In addition to …

We introduce a version of Koszul duality for categories, which extends the Koszul duality of
operads and right modules. We demonstrate that the derivatives which appear in Weiss …