Related papers: Category Theory for Programming
We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints…
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…
A general simplicity problem in category theory is proposed. A particular example, the simplest choice of generators of an algebra is specified and illustrated by an example.
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
The role of types in categorical models of meaning is investigated. A general scheme for how typed models of meaning may be used to compare sentences, regardless of their grammatical structure is described, and a toy example is used as an…
We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…
The recent trend in mathematics is towards a framework of abstract mathematical objects, rather than the more concrete approach of explicitly defining elements which objects were thought to consist of. A natural question to raise is whether…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an…
This paper proposes a formal cognitive framework for problem solving based on category theory. We introduce cognitive categories, which are categories with exactly one morphism between any two objects. Objects in these categories are…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads.…
This survey article is intended as an introduction to the recent categorical classification theorems of the three authors, restricting to the special case of the category of modules for a finite group.
In this article, we propose a Category Theory approach to (syntactic) interoperability between linguistic tools. The resulting category consists of textual documents, including any linguistic annotations, NLP tools that analyze texts and…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
Actions of monoidal categories on categories, also known as actegories, have been familiar to category theorists for a long time, and yet a comprehensive overview of this topic seems to be missing from the literature. Recently, actegories…
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
This thesis deals with two main topics: virtual double categories as semantics environments for predicate logic, and a syntactic presentation of virtual double categories as a type theory. One significant principle of categorical logic is…