Related papers: How to enhance categories, and why?

We introduce the notion of an enriched set, as an abstraction of enriched categories, and a category of enriched sets. The set of enriched sets is itself described as a set enriched over the category of enriched sets. We introduce a method…

Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.

We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.

We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. The aim of the paper is to justify and contextualize the new notion by…

In this paper we present background results in enriched category theory and enriched model category theory necessary for developing model categories of enriched functors suitable for doing functor calculus.

Enrichment and internal categories are two different way to generalize the notion of category. As such, enriching double categories (which are categories internal to Cat) is not a clear concepts. One can look at the internal categories of…

Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…

No new results. This is a short overview of the standard machinery of filtered colimits and accessible categories, written in parallel to a homotopically enhanced version available as Section 7.6 in arXiv:2409.17489.

We provide a definition of enrichment that applies to a wide variety of categorical structures, generalizing Leinster's theory of enriched $T$-multicategories. As a sample of newly enrichable structures, we describe in detail the examples…

We present a general procedure for constructing triangulated categories, linear over a field, with distinct enhancements. Some of our examples can be equipped with a (non-degenerate) t-structure, thereby showing that the existence of a…

This is essentially an illustration for the general technology of homotopical enhancements developed recently in arxiv:2409.17489. We take the derived category of an abelian category, and we look at the full subcategory spanned by complexes…

In this paper we introduce the theory of ends and coends in the context of enriched bicategories. This will be an enriched version of the theory introduced in [Cor16], and a bicategorical version of the classical theory of enriched…

This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…

This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…

These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.

This paper presents an original way to add new data in a reference dictionary from several other lexical resources, without loosing any consistence. This operation is carried in order to get lexical information classified by the sense of…

This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory -- categorifying the classical theory of categories enriched in a monoidal category -- up to a description of the free…

A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…

We collect in one place a variety of known and folklore results in enriched model category theory and add a few new twists. The central theme is a general procedure for constructing a Quillen adjunction, often a Quillen equivalence, between…

We thoroughly treat several familiar and less familiar definitions and results concerning categories, functors and distributors enriched in a base quantaloid Q. In analogy with V-category theory we discuss such things as adjoint functors,…