### 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 Postdoc in Mathematics

at University of Ottawa.

I work somewhere between category theory and the foundations of quantum computing. At the moment I'm interested in isotropy of algebraic theories, contextuality in quantum mechanics and quantum cryptography. I am also curious about higher category theory, type theory, 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 a well-behaved notion of a biproduct in any category without assuming pointedness.

Karvonen, M. (2020). Biproducts without pointedness. Cahiers de topologie et géométrie différentielle catégoriques, Vol LXI, Issue 3, 229-238.

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This is the extended version of the previous conference 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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