The language of∞-categories provides an insightful new way of expressing many results in
higher-dimensional mathematics but can be challenging for the uninitiated. To explain what …

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 …

Working in the context of symmetric spectra, we describe and study a homotopy completion
tower for algebras and left modules over operads in the category of modules over a …

We prove that the category of modules over a separable ring object in a tensor triangulated
category admits a unique structure of triangulated category which is compatible with the …

We give a survey of the ideas of descent and nilpotence, beginning with the theory of thick
subcategories. We focus on examples arising from chromatic homotopy theory (such as …

In the foundational logical framework of homotopy-type theory we discuss a natural
formalization of secondary integral transforms in stable geometric homotopy theory. We …

We show that the category of algebraically cofibrant objects in a combinatorial and simplicial
model category A has a model structure that is left-induced from that on A. In particular it …

Let 𝕂 be a comonad on a model category M. We provide conditions under which the
associated category M𝕂 of 𝕂‐coalgebras admits a model category structure such that the …

The settings for homotopical algebra—categories such as simplicial groups, simplicial rings,
A∞ spaces, E∞ ring spectra, etc.—are often equivalent to categories of algebras over some …

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 …