We prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal
model categories gives rise to a Quillen equivalence between their model categories of (non …

Simplicial spaces are analogues in the category of spaces of chain complexes (ie,
resolutions) in homological algebra. We study a novel way of doing “homotopy theory” with …

VOEVODSKY’S CRITERION FOR CONSTRUCTIBLE CATEGORIES OF COEFFICIENTS
Introduction 1 1. The motivic stable homotopy category 4 1. Page 1 VOEVODSKY’S CRITERION …

The first goal of this paper is to provide an abstract framework in which to formulate and
study local duality in various algebraic and topological contexts. For any stable∞-category C …

By combining ideas of homotopical algebra and of enriched category theory, we explain
how two classical formulas for homotopy colimits, one arising from the work of Quillen and …

We establish a relation between smooth 2-functors defined on the path 2-groupoid of a
smooth manifold and differential forms on this manifold. This relation can be understood as a …

Abstract We generalize Berger and Moerdijk's results on axiomatic homotopy theory for
operads to the setting of enriched symmetric monoidal model categories, and show how this …

Optics are bidirectional accessors of data structures; they provide a powerful abstraction of
many common data transformations. This abstraction is compositional thanks to a …

We develop a general theory of cosimplicial resolutions, homotopy spectral sequences, and
completions for objects in model categories, extending work of Bousfield–Kan and …

We define and study opfibrations of V-enriched categories when V is an extensive monoidal
category whose unit is terminal and connected. This includes sets, simplicial sets …