Related papers: Category Theory for Programming
We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to…
Motivated by potential applications to theoretical computer science, in particular those areas where the Curry-Howard correspondence plays an important role, as well as by the ongoing search in pure mathematics for feasible approaches to…
We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…
This thesis revolves around an area of computer science called "semantics". We work with operational semantics, equational theories, and denotational semantics. The first contribution of this thesis is a study of the commutativity of…
We give interpretations of some known key agreement protocols in the framework of category theory and in this way we give a method of constructing of many new key agreement protocols.
The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on…
We study the central objects of symbolic dynamics, that is, subshifts and block maps, from the perspective of basic category theory, and present several natural categories with subshifts as objects and block maps as morphisms. Our main…
It is informally understood that the purpose of modal type constructors in programming calculi is to control the flow of information between types. In order to lend rigorous support to this idea, we study the category of classified sets, a…
The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
We introduce Elgot categories, a sort of distributive monoidal category with additional structure in which the partial recursive functions are representable. Moreover, we construct an initial Elgot category, the morphisms of which coincide…
The first-order model theory of modules has been studied for decades. More recently, the model theoretic study of nonelementary classes of modules--especially Abstract Elementary Classes of modules--has produced interesting results. This…
The purpose of this dissertation is to set up a theory of generalized operads and multicategories, and to use it as a language in which to propose a definition of weak n-category. Included is a full explanation of why the proposed…
Differential categories were introduced to provide a minimal categorical doctrine for differential linear logic. Here we revisit the formalism and, in particular, examine the two different approaches to defining differentiation which were…
We study, in an abstract axiomatic setting, the notion of sectional category of a morphism. From this, we unify and generalize known results about this invariant in different settings as well as we deduce new applications.
In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to…
In this paper, a monad-based denotational model is introduced and shown adequate for the Proto-Quipper family of calculi, themselves being idealized versions of the Quipper programming language. The use of a monadic approach allows us to…
This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
The aim of the paper is to build a connection between two approaches towards categorical language theory: the coalgebraic and algebraic language theory for monads. For a pair of monads modelling the branching and the linear type we defined…