Related papers: Canonical Extensions of Quantale-Enriched Categori…
We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.
We define a canonical form for piecewise defined functions. We show that this has a wider range of application as well as better complexity properties than previous work.
Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set…
We formulate an elementary condition on an involutive quantaloid Q under which there is a distributive law from the Cauchy completion monad over the symmetrisation comonad on the category of Q-enriched categories. For such quantaloids,…
We characterize virtual double categories of enriched categories, functors, and profunctors by introducing a new notion of double-categorical colimits. Our characterization is strict in the sense that it is up to equivalence between virtual…
The canonical formalism for expanding metrics scenarios is presented. Non-unitary time evolution implied by expanding geometry is described as a trajectory over unitarily inequivalent representations at different times of the canonical…
A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable…
Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with…
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…
This is a companion overview paper to arXiv:2409.17489: we give all the main definitions, constructions and statements, but no proofs.
We generalize Barr's embedding theorem for regular categories to the context of enriched categories.
Dilatations modify categories by imposing that some morphisms factorize through some others. This is formalized by a universal property. This text is devoted to introduce and study this construction. Examples of dilatations of categories…
Building on our previous work on enriched universal algebra, we define a notion of enriched language consisting of function and relation symbols whose arities are objects of the base of enrichment. In this context, we construct atomic…
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.
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…
We define a mapping space for Gray-enriched categories adapted to higher gauge theory. Our construction differs significantly from the canonical mapping space of enriched categories in that it is much less rigid. The two essential…
We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in…
We investigate an enriched-categorical approach to a field of discrete mathematics. The main result is a duality theorem between a class of enriched categories (called $\overline{\mathbb{Z}}$- or $\overline{\mathbb{R}}$-categories) and that…
In this paper we consider a notion of pointwise Kan extension in double categories that naturally generalises Dubuc's notion of pointwise Kan extension along enriched functors. We show that, when considered in equipments that admit…
Enlarging on Parts I, II, and III we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of equations involving higher order derivatives. The motivation is that results and…