### A comonadic view of simulation and quantum resources

We simplify and generalize the ideas in the QPL paper below.

LiCS 2019

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a PhD student in Informatics

at University of Edinburgh.

I work somewhere between category theory and the foundations of quantum computing. At the moment I am moving to University of Ottawa to work on isotropy and on quantum cryptography. Besides this, I intend to keep working on quantum contextuality. My PhD research was on dagger categories and was done in Edinburgh, with Chris Heunen as my primary supervisor and Tom Leinster as my secondary supervisor. 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. This is what I look like on paper.

We simplify and generalize the ideas in the QPL paper below.

LiCS 2019

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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.

MFPS 2018

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

QPL 2018.

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

Heunen, C., & Karvonen, M. (2019). Limits in dagger categories. Theory and Applications of Categories, Vol. 34, No. 18, 468-513.

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

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