I work in the foundations of quantum computing, especially in category-theoretical approaches. At the moment I am mostly trying to understand and develop further the theory of dagger categories. I am also interested in reversible computing, type theory, categorical logic and more generally, in most parts of pure mathematics and theoretical computer science where an abstract, structural approach pays off.
My primary supervisor is Chris Heunen and Tom Leinster is my secondary supervisor. This is what I look like on paper.

## Papers

### Reversible effects as inverse arrows

We study (reversible) side-effects in a reversible programming language. As reversible computing can be modelled by inverse categories, we model side-effects using a notion of arrow suitable for inverse categories. Since inverse categories can be defined as certain dagger categories, we also develop a notion of a dagger arrow.

To appear in MFPS 2018.

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### Categories of empirical models

A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality.

To appear in QPL 2018.

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### Limits in dagger categories

We define a notion of limit suitable for dagger categories and explore it.

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### Biproducts without zero morphisms

Turns out one can define the notion of a biproduct in any category without assuming zero morphisms. If you can come up with more interesting new examples, I'd be happy to hear.

Submitted for publication.

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### Monads on dagger categories

This is the extended version of the previous paper.

Heunen, C., & Karvonen, M. (2016). Monads on dagger categories. Theory and Applications of Categories, Vol. 31, No. 35, 1016-1043.

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### Reversible monadic computing

Heunen, C., & Karvonen, M. (2015). Reversible monadic computing. Electronic Notes in Theoretical Computer Science, 319, 217-237.

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