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 …

Since the first draft of this text, which appeared in 2012 on the arXiv, the theory of higher
Segal spaces has been further developed in various directions by several groups of authors …

A common technique for producing a new model category structure is to lift the fibrations and
weak equivalences of an existing model structure along a right adjoint. Formally dual but …

We introduce the notion of an exact dg category, which is a simultaneous generalization of
the notions of exact category in the sense of Quillen and of pretriangulated dg category in …

This is an expository paper on homotopy colimits and homotopy limits. These are
constructions which should arguably be in the toolkit of every modern algebraic topologist …

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 …

As a step towards establishing homotopy-theoretic foundations for topological data analysis
(TDA), we introduce and study homotopy interleavings between filtered topological spaces …

We set up operadic foundations for equivariant iterated loop space theory. We start by
building up from a discussion of the approximation theorem and recognition principle for V …

The present note is a recollection of the most striking and useful applications of co/end
calculus. We put a considerable effort in making arguments and constructions rather explicit …

This chapter discusses non-technical account of some ideas in the theory of∞-categories,
as originally introduced by Boardman–Vogt in their study of homotopy-invariant algebraic …