113 citations · 1.3k across the 83 of their papers we have counts for
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On the functor l^2
Chris Heunen
We study the functor l^2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and its homsets are algebraic domain…
H*-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics
Samson Abramsky, Chris Heunen
A certain class of Frobenius algebras has been used to characterize orthonormal bases and observables on finite-dimensional Hilbert spaces. The presence of units in these algebras…
The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach
Chris Heunen, Nicolaas P. Landsman, Bas Spitters +1
We compare two influential ways of defining a generalized notion of space. The first, inspired by Gelfand duality, states that the category of 'noncommutative spaces' is the opposi…
Complementarity in categorical quantum mechanics
Chris Heunen
We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general cat…
Noncommutativity as a colimit
Benno van den Berg, Chris Heunen
Every partial algebra is the colimit of its total subalgebras. We prove this result for partial Boolean algebras (including orthomodular lattices) and the new notion of partial C*-…