Researcher · Director · Educator · Founder
Carlos
Zapata-Carratalá
My research focuses on the mathematical foundations of science, and today centres on Arity Science: mathematical and computational frameworks for higher-order systems, from n-ary algebras and hypergraphs to higher-arity categories.
CurrentlyResearch Director, Arity Science

Researching deep structure
Higher-arity algebra, hypergraphs and the foundations of mathematical physics.
Building communities
Founder of SEMF, the Society for Multidisciplinary and Fundamental Research.
Innovating in education
University lecturing, summer schools and the pedagogy of linear algebra.
Exploring audiovisual aesthetics
Harpsichord, improvisation, film, 3D art and game design.

Projects
Arity Science
Mathematical and computational frameworks for higher-order systems: n-ary algebras, hypergraphs and higher-arity categories.
arity.science →Game designEntropy Studios
The board and card game studio I founded in Alicante, home of Entropy TCG and Mine, Mine, Mine!. I lead its game design and direction.
Games →CommunitySEMF
The Society for Multidisciplinary and Fundamental Research, which I founded: colloquia, conferences and interdisciplinary summer schools.
semf.org.es →VolunteeringMission to Ukraine
Delivering a truck for medical evacuations and drone-detection equipment to Ukrainian defenders, documented on video.
Read more →Current role
Research Director, Arity Science
After leading the Causality, Observers and Computation project at the Wolfram Institute, I now pursue independent research as Research Director of Arity Science, a programme on the compositional structure of higher-order systems.
Recent publications
- Diagrammatic calculus and generalized associativity for higher-arity tensor operationsTheoretical Computer Science · 2024
- An Invitation to Higher Arity ScienceComplex Systems 32(4) · 2024
- Hypermatrix Algebra and Irreducible Arity in Higher-Order Systems: Concepts and PerspectivesAdvances in Complex Systems · 2023
- Biunit pairs in semiheaps and associated semigroupsSemigroup Forum · 2023