Related papers: A Categorical Integration of Quantifiers:A Higher …
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
We introduce the notion of weighted limit in an arbitrary quasi-category, suitably generalizing ordinary limits in a quasi-category, and classical weighted limits in an ordinary category. This is accomplished by generalizing Joyal's…
Deep learning, despite its remarkable achievements, is still a young field. Like the early stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad-hoc design decisions, and the lack of a uniform and…
This paper proposes a novel approach to semantic ontology alignment using contextual descriptors. A formalization was developed that enables the integration of essential and contextual descriptors to create a comprehensive knowledge model.…
In the framework of Category Theory, we study the association between finite--dimensional representations of a compact quantum group and quantum vector bundles with linear connections for a given quantum principal bundle with a principal…
This article serves as a preliminary introduction to the design of a new, open-source applied and computational category theory framework, named Categorica, built on top of the Wolfram Language. Categorica allows one to configure and…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
We show that small quasicategories embed, both simplicially and 2-categorically, into prederivators defined on arbitrary small categories, so that in some senses prederivators can serve as a model for $(\infty,1)$-categories. The result for…
The question "What is category theory" is approached by focusing on universal mapping properties and adjoint functors. Category theory organizes mathematics using morphisms that transmit structure and determination. Structures of…
In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…
We propose a framework for constructing and analyzing multiclass and multioutput classification metrics, i.e., involving multiple, possibly correlated multiclass labels. Our analysis reveals novel insights on the geometry of feasible…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
We present the notion of "cyclic double multicategory", as a structure in which to organise multivariable adjunctions and mates. The classic example of a 2-variable adjunction is the hom/tensor/cotensor trio of functors; we generalise this…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
Disentangling the explanatory factors in complex data is a promising approach for generalizable and data-efficient representation learning. While a variety of quantitative metrics for learning and evaluating disentangled representations…
We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object. Coproducts in the original category are described in its quotient by our new weaker notion of a 'phased coproduct'. We examine…
We present a doctrinal approach to category theory, obtained by abstracting from the indexed inclusions (via discrete fibrations and opfibrations) of the left and of the right actions of X in Cat in categories over X. Namely, a "weak…