Related papers: Quantale-Enriched Multicategories Via Actions
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.
This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories…
Our subject is that of categories, functors and distributors enriched in a base quantaloid Q. We show how cocomplete Q-categories are precisely those which are tensored and conically cocomplete, or alternatively, those which are tensored,…
We describe a duality for quantale-enriched categories that extends the Lawson duality for continuous dcpos: for any saturated class J of modules that commute with certain weighted limits, and under an appropriate choice of morphisms, the…
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,…
By introducing the concept of quantaloidal completions for an order-enriched category, relationships between the category of quantaloids and the category of order-enriched categories are studied. It is proved that quantaloidal completions…
Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey…
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…
It is shown that every two-variable adjunction in categories enriched in a commutative quantale serves as a base for constructing Isbell adjunctions between functor categories, and Kan adjunctions are precisely Isbell adjunctions…
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory.…
With quantaloids carefully constructed from multi-adjoint frames, it is shown that multi-adjoint concept lattices, multi-adjoint property-oriented concept lattices and multi-adjoint object-oriented concept lattices are derivable from Isbell…
The familiar adjunction between ordered sets and completely distributive lattices can be extended to generalised metric spaces, that is, categories enriched over a quantale (a lattice of "truth values"), via an appropriate distributive law…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
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…
Categories enriched over a commutative unital quantale can be studied as generalized, or many-valued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain…
Each distributor between categories enriched over a small quantaloid Q gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to two monads. These two adjunctions are respectively…
Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…
We define the phrase `category enriched in an fc-multicategory' and explore some examples. An fc-multicategory is a very general kind of 2-dimensional structure, special cases of which are double categories, bicategories, monoidal…
Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of…
We apply the quantization scheme introduced in [arXiv:1204.2870] to a particle on a circle. We find that the quantum action functional restricted to appropriate coherent states can be expressed as the classical action plus…