8 results
Bart Jacobs.
The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier work). It is illustrated how such coalgebras-on-algebras can be […]
Published on September 18, 2013
Bart Jacobs.
This paper is a sequel to arXiv:0902.2355 and continues the study of quantum logic via dagger kernel categories. It develops the relation between these categories and both orthomodular lattices and Foulis semigroups. The relation between the latter two notions has been uncovered in the 1960s. The […]
Published on June 18, 2010
Robert W. J. Furber ; Bart P. F. Jacobs.
C*-algebras form rather general and rich mathematical structures that can be studied with different morphisms (preserving multiplication, or not), and with different properties (commutative, or not). These various options can be used to incorporate various styles of computation (set-theoretic, […]
Published on June 10, 2015
Bart Jacobs ; Frédéric Vogels ; Frank Piessens.
VeriFast is a leading research prototype tool for the sound modular verification of safety and correctness properties of single-threaded and multithreaded C and Java programs. It has been used as a vehicle for exploration and validation of novel program verification techniques and for industrial […]
Published on September 22, 2015
Bart Jacobs.
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of effect algebra/module that emerged in theoretical physics form […]
Published on October 1, 2015
Bart Jacobs.
In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an adjunction between state- and predicate-transformers. The […]
Published on May 17, 2017
Bart Jacobs.
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation. A novel description of normalisation is given as a […]
Published on August 29, 2017
Bart Jacobs ; Abraham Westerbaan.
This paper gives a systematic account of various metrics on probability distributions (states) and on predicates. These metrics are described in a uniform manner using the validity relation between states and predicates. The standard adjunction between convex sets (of states) and effect modules (of […]
Published on February 25, 2020