arXiv subjects

Krzysztof Bar

Publications and source records attributed to Krzysztof Bar.

4 recordsLinked to original sources

arXiv2018

Globular: an online proof assistant for higher-dimensional rewriting

This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their construction with a point-and- click interface, and performs type checking to prevent incorrect rewrites. Hosted on the web, it has a low barrier to use, and allows hyperlinking of formalized proofs directly from research papers. It allows the formalization of proofs from logic, topology and algebra which are not formalizable by other methods, and we give several examples.

cs.LO↗

arXiv2016

Data structures for quasistrict higher categories

We present new data structures for quasistrict higher categories, in which associativity and unit laws hold strictly. Our approach has low axiomatic complexity compared to traditional algebraic definitions of higher categories, and we use it to give a practical definition of quasistrict 4-category. It is also amenable to computer implementation, and we exploit this to give a new machine-verified algebraic proof that every adjunction of 1-cells in a quasistrict 4-category can be promoted to a coherent adjunction satisfying the butterfly equations.

math.CT↗

arXiv2014

A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem

This paper explores the use of 2-categorical technology for describing and reasoning about complex quantum procedures. We give syntactic definitions of a family of complementary measurements, and of quantum key distribution, and show that they are equivalent. We then show abstractly that either structure gives a solution to the Mean King problem, which we also formulate 2-categorically.

cs.LO↗

arXiv2014

Groupoid Semantics for Thermal Computing

A groupoid semantics is presented for systems with both logical and thermal degrees of freedom. We apply this to a syntactic model for encryption, and obtain an algebraic characterization of the heat produced by the encryption function, as predicted by Landauer's principle. Our model has a linear representation theory that reveals an underlying quantum semantics, giving for the first time a functorial classical model for quantum teleportation and other quantum phenomena.

cs.LO↗