Applied Category Theorist

Kodamai Limited; Glasgow; On-site; GBP 70,000 - 120,000; Full time

Benefits offered by this job

Equity participation

Glasgow HQ with flexible working

Research budget

30 days annual leave

Private healthcare

Freedom to publish

Job summary

Kodamai Limited is seeking a researcher to formalise categorical structures for its agent orchestration model, translating theory into practical system designs. You will work at the frontier of applied mathematics and AI systems, publishing in academic venues and guiding junior researchers.

The role emphasizes deep category theory expertise, strong mathematical communication, and a drive to deploy theory in real-world scalable systems from our Glasgow HQ with flexible working arrangements.

Qualifications

• PhD in mathematics, theoretical computer science, or a closely related field.
• Deep expertise in category theory — functors, natural transformations, adjunctions, monads, and beyond.
• Published research or demonstrable original contributions to applied mathematics or formal methods.
• Ability to communicate complex mathematics clearly to both academic and engineering audiences.
• Strong interest in real-world deployment — theory in service of systems that need to work.

Responsibilities

• Develop and formalise the categorical structures underlying Kodamai's agent orchestration model.
• Collaborate with engineers to translate formal specifications into implementable designs.
• Advance Kodamai's neuro-symbolic architecture through original research.
• Author internal technical papers and contribute to external academic publications.
• Mentor and support junior researchers and engineers working on formal methods.
• Engage with the academic community on behalf of Kodamai at conferences and workshops.

Skills

Category theory

Mathematics

Research communication

Theoretical computer science

Education

PhD in mathematics or related field

Tools

Coq

Lean 4

Agda

Job description

Kodamai is built on the proposition that category theory is the correct mathematical foundation for safe, composable multi-agent AI. We are looking for a researcher who believes this too — and who wants to spend their time proving it. You will work at the frontier of applied mathematics and AI systems design, translating deep theoretical insights into the formal foundations of our platform.

Key Responsibilities

• Develop and formalise the categorical structures underlying Kodamai's agent orchestration model
• Collaborate with engineers to translate formal specifications into implementable designs
• Advance Kodamai's neuro-symbolic architecture through original research
• Author internal technical papers and contribute to external academic publications
• Mentor and support junior researchers and engineers working on formal methods
• Engage with the academic community on behalf of Kodamai at conferences and workshops

Qualifications and Requirements

• PhD in mathematics, theoretical computer science, or a closely related field
• Deep expertise in category theory — functors, natural transformations, adjunctions, monads, and beyond
• Published research or demonstrable original contributions to applied mathematics or formal methods
• Ability to communicate complex mathematics clearly to both academic and engineering audiences
• Strong interest in real-world deployment — theory in service of systems that need to work

Preferred Qualifications

• Experience with dependent type theory, homotopy type theory, or topos theory
• Familiarity with proof assistants: Coq, Lean 4, Agda, or similar
• Prior work on categorical semantics for programming languages or concurrency
• Interest in AI safety, formal verification, or regulated systems

What We Offer

• Competitive salary with meaningful equity participation
• Based at our Glasgow HQ with flexible working arrangements
• Dedicated research budget — conferences, journals, compute resources
• Close collaboration with a founding team drawn from world-class academic institutions
• Freedom to publish and contribute to the academic community
• 30 days annual leave and private healthcare

If this sounds like you, we'd love to hear from you.

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