4 papers
Hilbert -categories: Where limits in analysis and category theory meet
Matthew Di Meglio, Chris Heunen
This article introduces Hilbert -categories: an abstraction of categories with similar algebraic and analytic properties to the categories of real, complex, and quaternionic Hil…
Dagger categories of relations: The equivalence of dilatory dagger categories and epi-regular independence categories
Matthew Di Meglio, Chris Heunen, Jean-Simon Pacaud Lemay +2
Several categories look like categories of relations, but do not fit the established theory of relations in regular categories. They include the category of surjective multivalued…
Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions
Matthew Di Meglio, Chris Heunen
We unravel a deep connection between limits of real numbers and limits in category theory. Using a new variant of the classical characterisation of the real numbers, we characteris…
Pre-Hilbert -categories: The Hilbert-space analogue of abelian categories
Matthew Di Meglio
This article introduces pre-Hilbert -categories: an abstraction of categories exhibiting "algebraic" aspects of the theory of Hilbert spaces. Notably, finite biproducts in pre-H…