Search

• < Previous
• 1
• Next >

---

Bases as Coalgebras

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&nbsp;[&hellip;]

---

Generic Trace Semantics via Coinduction

Ichiro Hasuo ; Bart Jacobs ; Ana Sokolova.

Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these "trace semantics," namely coinduction in a Kleisli&nbsp;[&hellip;]

---

Orthomodular lattices, Foulis Semigroups and Dagger Kernel Categories

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&nbsp;[&hellip;]

---

Hyper Normalisation and Conditioning for Discrete Probability Distributions

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&nbsp;[&hellip;]

---

Distances between States and between Predicates

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&nbsp;[&hellip;]

---

A Recipe for State-and-Effect Triangles

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&nbsp;[&hellip;]

---