# A Categorical Construction for the Computational Definition of Vector Spaces

@article{DazCaro2020ACC, title={A Categorical Construction for the Computational Definition of Vector Spaces}, author={Alejandro D{\'i}az-Caro and Octavio Malherbe}, journal={Applied Categorical Structures}, year={2020}, pages={1-38} }

Lambda- $${\mathcal {S}}$$ S is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi. One is to forbid duplication of variables, while the other is to consider all lambda-terms as algebraic linear functions. The type system of Lambda- $${\mathcal {S}}$$ S has a constructor S such that a type A is considered as the base of a vector space while S ( A ) is its span. Lambda- $${\mathcal {S}}$$ S can also be seen as a language for the… Expand

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Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model

- Computer Science, Mathematics
- ArXiv
- 2020

This paper introduces a valid subset of typing rules, defining an expressive enough quantum calculus, and proposes a categorical semantics for it, which consists of an adjunction between the category of semi-vector spaces of value distributions and the categories of sets of value distribution. Expand

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