Given a locally coherent Grothendieck category G, we prove that the homotopy category of
complexes of injective objects (also known as the coderived category of G) is compactly …

For a locally presentable abelian category B with a projective generator, we construct the
projective derived and contraderived model structures on the category of complexes …

A full subcategory of a Grothendieck category is called deconstructible if it consists of all
transfinite extensions of some set of objects. This concept provides a handy framework for …

We give a general parametrization of all the recollement data for a triangulated category with
a set of generators. From this we deduce a characterization of when a ℵ0-perfectly …

We construct a model structure on the category of small categories enriched over a
combinatorial closed symmetric monoidal model category satisfying the monoid axiom …

We develop a theory of categories which are simultaneously (1) indexed over a base
category S with finite products, and (2) enriched over an S-indexed monoidal category V …

We describe a sufficient condition on a finitely complete and cocomplete lextensive category
X, under which the categorical smash product provides a canonical (symmetric, distributive …

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 …

We prove a rectification theorem for enriched∞–categories: if V is a nice monoidal model
category, we show that the homotopy theory of∞–categories enriched in V is equivalent to …

We prove that, in a triangulated category with combinatorial models, every localizing
subcategory is coreflective and every colocalizing subcategory is reflective if a certain large …