Related papers: Chu connections and back diagonals between $\mathc…
For a small quantaloid $\mathcal{Q}$, it is shown that the category of $\mathcal{Q}$-distributors and diagonals is equivalent to a quotient category of the category of $\mathcal{Q}$-interior spaces and continuous $\mathcal{Q}$-distributors.…
It is shown that, for a small quantaloid Q, the category of small Q-categories and Q-functors is total and cototal, and so is the category of Q-distributors and Q-Chu transforms.
This dissertation is devoted to a study of adjunctions concerning categories enriched over a quantaloid Q (or Q-categories for short), with the following types of adjunctions involved: (1) adjoint functors between Q-categories; (2) adjoint…
The scientific and practical needs of the twenty-first century lead humankind to convergence of the specialized and diverse branches of science and technology. This convergence reveals the need for new mathematical theories capable of…
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,…
We investigate monoidal categories of formal contexts, in which states correspond to formal concepts. In particular we examine the category of bonds or Chu correspondences between contexts, which is known to be equivalent to the…
For a small quantaloid $\mathcal{Q}$, a $\mathcal{Q}$-closure space is a small category enriched in $\mathcal{Q}$ equipped with a closure operator on its presheaf category. We investigate $\mathcal{Q}$-closure spaces systematically with…
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…
A folklore result in category theory is that a (weakly) Cartesian closed category with finite co-products is distributive. Usually, the proof of this small result is carried on using the fact that the exponential functor is right adjoint to…
Linearly distributive categories were introduced to model the tensor/par fragment of linear logic, without resorting to the use of negation. Linear bicategories are the bicategorical version of linearly distributive categories. Essentially,…
The theory of distributed conceptual structures, as outlined in this paper, is concerned with the distribution and conception of knowledge. It rests upon two related theories, Information Flow and Formal Concept Analysis, which it seeks to…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension…
For any small quantaloid $\Q$, there is a new quantaloid $\D(\Q)$ of diagonals in $\Q$. If $\Q$ is divisible then so is $\D(\Q)$ (and vice versa), and then it is particularly interesting to compare categories enriched in $\Q$ with…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
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,…
In this communication, one shows that there exists in the literature a certain form of deformed derivative that can here be identified as the dual of conformable derivative. The deformed subtraction is used here, together with the duality…
The notion of relative derived category with respect to a subcategory is introduced. A triangle-equivalence, which extends a theorem of Gao and Zhang [Gorenstein derived categories, \emph{J. Algebra} \textbf{323} (2010) 2041-2057] to the…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…