Related papers: Category Theory Using String Diagrams

String diagrams are pictorial representations for morphisms of symmetric monoidal categories. They constitute an intuitive and expressive graphical syntax, which has found application in a very diverse range of fields including concurrency…

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…

Polynomial functors are useful in the theory of data types, where they are often called containers. They are also useful in algebra, combinatorics, topology, and higher category theory, and in this broader perspective the polynomial aspect…

Distributed word representations have been demonstrated to be effective in capturing semantic and syntactic regularities. Unsupervised representation learning from large unlabeled corpora can learn similar representations for those words…

Investment returns naturally reside on irregular domains, however, standard multivariate portfolio optimization methods are agnostic to data structure. To this end, we investigate ways for domain knowledge to be conveniently incorporated…

We define the notion of an indexed profunctor over a 2-category, and use it to develop an abstract theory of limits. The theory subsumes (conical) limits, weighted limits, ends and Kan extensions. Results include an abstract version of the…

In this paper, we propose a framework for graph signal processing using category theory. The aim is to generalize a few recent works on probabilistic approaches to graph signal processing, which handle signal and graph uncertainties.

The generality and pervasiness of category theory in modern mathematics makes it a frequent and useful target of formalization. It is however quite challenging to formalize, for a variety of reasons. Agda currently (i.e. in 2020) does not…

Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…

Framed combinatorial topology is a recent approach to tame geometry which expresses higher-dimensional stratified spaces via tractable combinatorial data. The resulting theory of spaces is well-behaved and computable. In this paper we…

In mathematical applications, category theory remains a contentious issue, with enthusiastic fans and a skeptical majority. In a muted form this split applies to the authors of this note. When we learned that the only mathematically sound…

Causal loop and stock and flow diagrams are broadly used in System Dynamics because they help organize relationships and convey meaning. Using the analytical work of Schoenberg (2019) to select what to include in a compressed model, this…

Probabilistic models over strings have played a key role in developing methods allowing indels to be treated as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do…

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…

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…

Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…

We present a novel approach to the concept of gluing in mathematics by introducing the notions of a gluing data category and a gluing data functor. Our work provides a formal categorical characterization of the notion of gluing in algebraic…

Category Theory is a well-known powerful mathematical modeling language with a wide area of applications in mathematics and computer science, including especially the semantical foundations of topics in software science and development.…

`Categorification' is the process of replacing equations by isomorphisms. We describe some of the ways a thoroughgoing emphasis on categorification can simplify and unify mathematics. We begin with elementary arithmetic, where the category…

Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…