H*-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics
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 means that they can…
ON ENDOMORPHISM ALGEBRAS OF SEPARABLE MONOIDAL FUNCTORS
We show that the (co)endomorphism algebra of a suciently separable \bre" functor into Vectk, for k a eld of characteristic 0, has the structure of what we call a \unital" von Neumann core in Vectk.…
Quantum groups and representations of monoidal categories
- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
This paper is intended to make explicit some aspects of the interactions which have recently come to light between the theory of classical knots and links, the theory of monoidal categories,…
The algebra of entanglement and the geometry of composition
The ZW calculus is presented, the first complete diagrammatic axiomatisation of the theory of qubits, and a notion of regular polygraph is proposed, barring cell boundaries that are not homeomorphic to a disk of the appropriate dimension, and the existence of weak units is equivalent to a representability property.
Let C be a category with finite colimits, writing its coproduct +, and let (D,⊗) be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided…
Rewriting modulo symmetric monoidal structure
- Computer Science2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
This paper interprets diagrams combinatorially as typed hypergraphs and establishes the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hyper graphs, subject to a soundness condition called convexity, on the other.
Restriction categories I: categories of partial maps
- MathematicsTheor. Comput. Sci.
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The separable Galois theory of commutative rings
Separability Separable fields Separable rings Separable schemes Separable polynomials Module projective algebras Idempotents and Profinite Spaces Boolean algebras and idempotents Profinite spaces…
Separable algebras over commutative rings
Preliminaries.- Central separable algebras and the brauer group.- Galois theory.- The six-term exact sequence.- Applications and remarks.
Bicategories of partial maps
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CORRESPONDENCES, MOTIFS AND MONOIDAL TRANSFORMATIONS