Related papers: How to enhance categories, and why?
Restriction categories were introduced as a way of generalising the notion of partial map categories. In this paper, we define cocomplete restriction category, and give the free cocompletion of a small restriction category as a suitably…
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…
This thesis is devoted to the proof of a theorem showing the existence of a closed model category structure for weakly enriched categories. It requires first of all the definitions of weakly enriched categories and equivalences of weakly…
The study of categories that abstract the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper strives to provide a modern presentation of these…
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…
Real-enriched categories are categories with real numbers as enrichment. Precisely, a real-enriched category is a category enriched over the commutative and unital quantale composed of the unit interval and a continuous t-norm. These notes…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
The objective of this paper is to provide a fairly general model category context in which one can perform Goodwille Calculus. There are two main parts to the paper, the first establishing general conditions which guarantee the existence of…
A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…
Inspired by the intrinsic formality of graded algebras, we prove a necessary and sufficient condition for strongly uniqueness of DG-enhancements. This approach offers a generalization to linearity over any commutative ring. In particular,…
Wikipedia is a useful knowledge source that benefits many applications in language processing and knowledge representation. An important feature of Wikipedia is that of categories. Wikipedia pages are assigned different categories according…
A number of exciting advances have been made in automated fact-checking thanks to increasingly larger datasets and more powerful systems, leading to improvements in the complexity of claims which can be accurately fact-checked. However,…
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…
In this supplementary appendix we provide additional results, omitted proofs and extensive simulations that complement the analysis of the main text (arXiv:1201.0224).
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
In this work, we explore a double categorical framework for categories of enriched graphs, categories and the newly introduced notion of cocategories. A fundamental goal is to establish an enrichment of V-categories in V-cocategories, which…
Refinement types enrich a language's type system with logical predicates that circumscribe the set of values described by the type, thereby providing software developers a tunable knob with which to inform the type system about what…
Invited contribution to the Encyclopedia of Mathematical Physics. We give an introduction to the homotopical theory of higher categories, focused on motivating the definitions of the basic objects, namely $\infty$-categories and…
We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…
We give an easy example of a triangulated category, linear over a field $k$, with two different enhancements, linear over $k$, answering a question of Canonaco and Stellari.