Related papers: Coend Optics for Quantum Combs
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…
For a relational Horn theory $\mathbb{T}$, we provide useful sufficient conditions for the exponentiability of objects and morphisms in the category $\mathbb{T}\text{-}\mathsf{Mod}$ of $\mathbb{T}$-models; well-known examples of such…
Computation can be considered by taking into account two dimensions: extensional versus intensional, and sequential versus concurrent. Traditionally sequential extensional computation can be captured by the lambda-calculus. However, recent…
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…
Combinatorial interpretation of the fibonomial coefficients as a number of choices of specific finite subsets of an infinite partially ordered set of not binomial type is proposed. This partially ordered set is here defined via…
The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics.…
We develop a functorial approach to the study of $n$-abelian categories by reformulating their axioms in terms of their categories of finitely presented functors. Such an approach allows the use of classical homological algebra and…
The set of integer number lists with finite length, and the set of binary trees with integer labels are both countably infinite. Many inductively defined types also have countably many elements. In this paper, we formalize the syntax of…
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…
This paper introduces an expressive class of quotient-inductive types, called QW-types. We show that in dependent type theory with uniqueness of identity proofs, even the infinitary case of QW-types can be encoded using the combination of…
We construct a model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical…
A Q-system in a C* 2-category is a unitary version of a separable Frobenius algebra object and can be viewed as a unitary version of a higher idempotent. We define a higher unitary idempotent completion for C* 2-categories called Q-system…
Bicategories of spans are characterized as cartesian bicategories in which every comonad has an Eilenberg-Moore ob ject and every left adjoint arrow is comonadic.
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
We give sufficient conditions for the existence of a Quillen model structure on small categories enriched in a given monoidal model category. This yields a unified treatment for the known model structures on simplicial, topological, dg- and…
We define generalized bialgebras and Hopf algebras and on this basis we introduce quantum categories and quantum groupoids. The quantization of the category of linear (super)spaces is constructed. We establish a criterion for the classical…
This paper is a sequel to "Logical systems I: Lambda calculi through discreteness". It provides a general 2-categorical setting for extensional calculi and shows how intensional and extensional calculi can be related in logical systems. We…
We explore an alternative definition of unit in a monoidal category originally due to Saavedra: a Saavedra unit is a cancellative idempotent (in a 1-categorical sense). This notion is more economical than the usual notion in terms of…
We provide bar and cobar constructions as functors between some categories of curved algebras and curved augmented coalgebras over a graded commutative ring. These functors are adjoint to each other.
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…