Related papers: Canonical Extensions of Quantale-Enriched Categori…
A coextensive category can be defined as a category $\mathcal{C}$ with finite products such that for each pair $X,Y$ of objects in $\mathcal{C}$, the canonical functor $\times\colon X/\mathcal{C} \times Y/\mathcal{C} \to (X \times…
We make a few remarks concerning pointwise extensions in a bicategory which include the case of bicategories of enriched categories. We show that extensions, pointwise or not, can be replaced by extensions along very special fully faithful…
We develop an extension of valuations theorem for suitable extensions of idempotent semirings. As an application, we give a new proof for the classical case of fields. Along the way, we develop characteristic one analogues of some central…
We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
We revisit the definition of Cartesian differential categories, showing that a slightly more general version is useful for a number of reasons. As one application, we show that these general differential categories are comonadic over…
A new construction to associate an internal category to an enriched one is presented. The key concept is that of extensive ambient category, and the construction follows the one that associates a category whose idempotents split to a given…
We continue the study of enriched infinity categories, using a definition equivalent to that of Gepner and Haugseng. In our approach enriched infinity categories are associative monoids in an especially designed monoidal category of…
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…
Categories can be identified -- up to isomorphism -- with polynomial comonads on Set. The left Kan extension of a functor along itself is always a comonad -- called the density comonad -- so it defines a category when its carrier is…
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…
The term Stone-type duality often refers to a dual equivalence between a category of lattices or other partially ordered structures on one side and a category of topological structures on the other. This paper is part of a larger endeavour…
The finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.
We propose a way to encode acceleration directly into quantum fields, establishing a new class of fields. Accelerated quantum fields, as we have named them, have some very interesting properties. The most important is that they provide a…
In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…
We define the twisted tensor product of two enriched categories, which generalizes various sorts of `products' of algebraic structures, including the bicrossed product of groups, the twisted tensor product of (co)algebras and the double…
We define the notion of an enriched Reedy category, and show that if A is a C-Reedy category for some symmetric monoidal model category C and M is a C-model category, the category of C-functors and C-natural transformations from A to M is…
We characterize injective objects, injective hulls and essential embeddings in the category of symmetric categories enriched in a small, integral and involutive quantaloid. In particular, injective partial metric spaces are precisely…
We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.
In this short survey article we collect the current state of the art in the nascent field of \textit{quantum enhancements}, a type of knot invariant defined by collecting values of quantum invariants of knots with colorings by various…