Carlos Zapata-Carratalá 2023-07-15 Carlos Zapata-Carratalá 2023-07-15

Hypermatrix Algebra and Irreducible Arity in Higher-Order Systems: Concepts and Perspectives

Carlos Zapata-Carratalá, Maximilian Schich, Taliesin Beynon, Xerxes D. Arsiwalla

Hypergraph and hypermatrix methods are applied to detect irreducible interactions in higher-order systems.

Jonathan Gorard 2022-10-13 Jonathan Gorard 2022-10-13

A Functorial Perspective on (Multi)computational Irreducibility

Jonathan Gorard

This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding category of (1-dimensional) cobordisms.

Carlos Zapata-Carratalá 2022-05-01 Carlos Zapata-Carratalá 2022-05-01

Heaps of Fish: arrays, generalized associativity and heapoids

Carlos Zapata-Carratala, Xerxes D. Arsiwalla, Taliesin Beynon

In this paper we investigate a ternary generalization of associativity by defining a diagrammatic calculus of hypergraphs that extends the usual notions of tensor networks, categories and relational algebras. In doing so we rediscover the ternary structures known as heaps and are able to give a more comprehensive treatment of their mergence in the context of dagger categories and their generalizations.