Related papers: Aspects of categorical recursion theory
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…
Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…
We provide a framework for abstract reconstruction problems using the $K$-theory of categories with covering families, which we then apply to reformulate the edge reconstruction conjecture in graph theory. Along the way, we state some…
We present a new, category theoretic point of view on finite Ramsey theory. Our aims are as follows: -- to define the category theoretic notions needed for the development of finite Ramsey Theory, -- to state, in terms of these notions, the…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
A definition of summability is put forward in the framework of general Carleman ultraholomorphic classes in sectors, so generalizing $k-$summability theory as developed by J.-P. Ramis. Departing from a strongly regular sequence of positive…
It is well known that general recursion cannot be expressed within Martin-Loef's type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
A collection of brilliant and original unfinished ideas by Wladyslaw Marcinek (1952-2003) in particle interactions, categorical approach to generalized statistics, qubits and quantum logic, entwined operators, cobordisms and noncommutative…
The paper presents an enriched categorical account of homological perturbation theory, including the formulation, proof and functoriality properties of the homological perturbation lemma.
We give results and observations which allow the application of the logarithmic tensor category theory of Lepowsky, Zhang and the author ([HLZ1]--[HLZ9]) to more general vertex (operator) algebras and their module categories than those…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
We present an overview of selected topics in random permutations and random partitions highlighting analogies with random matrix theory.
The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the possible connections between physical…
We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category of groups. We show how this notion provides a new approach to the categorical-algebraic question of the…
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…