Related papers: On pointwise Kan extensions in double categories

We discuss generalised duality theory for monoidal categories and its applications to the categories of exact endofunctors, graded vector spaces, and topological vector spaces.

We describe a 2-dimensional analogue of track categories, called two-track categories, and show that it can be used to model categories enriched in 2-type mapping spaces. We also define a Baues-Wirsching type cohomology theory for track…

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…

We investigate fundamental properties of adjoint functors to the precomposition functor in the category of strict polynomial functors.

In this article the notion of virtual double category (also known as fc-multicategory) is extended as follows. While cells in a virtual double category classically have a horizontal multi-source and single horizontal target, the notion of…

The existence of adjoints to algebraic functors between categories of models of Lawvere theories follows from finite-product-preservingness surviving left Kan extension. A result along these lines was proved in Appendix 2 of Brian Day's…

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence…

In this paper we introduce and investigate the notions of diagrams and discrete extensions in the study of finitary $2$-representations of finitary $2$-categories.

This paper contains results from two areas -- formal theory of Kan extensions and concrete categories. The contribution to the former topic is based on the extension of the concept of Kan extension to the cones and we prove that limiting…

The basic concepts in category theory are representables, adjoints, limits, and monads. In this talk, we define the notion of a Kan extension and show that this notion encompasses these concepts.

Category theory has become central to certain aspects of theoretical physics. Bain [Synthese, 190:1621--1635 (2013)] has recently argued that this has significance for ontic structural realism. We argue against this claim. In so doing, we…

What has category theory to offer to Banach spacers? In this second part survey-like paper we will focus on very much needed advanced categorical and homological elements, such as Kan extensions, derived category and derived functor or…

This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.

We investigate categories in which products distribute over coproducts, a structure we call doubly-infinitary distributive categories. Through a range of examples, we explore how this notion relates to established concepts such as…

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…

Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalization of the theory of canonical extension to the setting of first order logic. We define a notion of…

We define 2-categories of microlocal perverse (resp. coherent) sheaves of categories on the skeleton of a hypertoric variety and show that the generators of these 2-categories lift the projectives (resp. simples) in hypertoric category…

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…

For a commutative quantale $\mathcal{V}$, the category $\mathcal{V}-cat$ can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor $T$ (formalised as an endofunctor on sets) can be…

Structured and decorated cospans are broadly applicable frameworks for building bicategories or double categories of open systems. We streamline and generalize these frameworks using central concepts of double category theory. We show that,…