Related papers: Enhanced finite triangulated categories
We give criteria for subcategories of a compactly generated algebraic triangulated category to be precovering or preenveloping. These criteria are formulated in terms of closure conditions involving products, coproducts, directed homotopy…
This is a companion overview paper to arXiv:2409.17489: we give all the main definitions, constructions and statements, but no proofs.
We continue the study of enriched infinity categories, using a definition equivalent to that of Gepner and Haugseng. In our approach enriched infinity categories are associative monoids in an especially designed monoidal category of…
Given a fixed tensor triangulated category S we consider triangulated categories T together with an S-enrichment which is compatible with the triangulated structure of T. It is shown that, in this setting, an enriched analogue of Brown…
We introduce the notion of an enriched fibration, i.e. a fibration whose total category and base category are enriched in those of a monoidal fibration in an appropriate way. Furthermore, we provide a way to obtain such a structure,…
Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full…
We develop the general formalism of approximable triangulated categories, and prove two representability theorems.
We show that the class of profinite duality groups is closed under group extensions provided that the kernel satisfies some finiteness condition. This extends earlier results of Pletch and of Wingberg.
On objects of a triangulated category with a stability condition, we construct a topology.
The singularity category of a ring detects the homological singularity of the given ring, and appears in many different contexts. We describe two different dg enhancements of the singularity category, that is, the Vogel dg category and the…
We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism…
The importance of accessible categories has been widely recognized; they can be described as those freely generated in some precise sense by a small set of objects and, because of that, satisfy many good properties. More specifically…
We develop the theory of tricategorical limits and colimits, and show that they can be modelled up to biequivalence via certain homotopically well-behaved limits and colimits enriched over the monoidal model category $\mathbf{Gray}$ of…
Continuing the investigations by the author \cite{SchnurrWM} and Glasner and Weiss \cite{GlasnerWeiss} on generic properties of extensions, we give a sufficient condition for the strongly mixing extensions of a fixed transformation to be of…
Enriched categories are categories whose sets of morphisms are enriched with extra structure. Such categories play a prominent role in the study of higher categories, homotopy theory, and the semantics of programming languages. In this…
We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring…
This paper presents a necessary and sufficient condition on a category with weak finite limits for its exact completion to be (locally) cartesian closed. A paper by Carboni and Rosolini already claimed such a characterisation using a…
We investigate the homological behaviour of compactly generated triangulated categories under separable extensions. We show that homological invariants (finiteness of global dimension, gorensteinness and regularity) are preserved under such…
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.
Restriction categories were introduced to provide an axiomatic setting for the study of partially defined mappings; they are categories equipped with an operation called restriction which assigns to every morphism an endomorphism of its…