Categorical simulations

A Categorical Approach to Simulations

Simulations are a very natural way of relating concurrent systems, which are mathematically modeled by Kripke structures. The range of available notions of simulations makes it very natural to adopt a categorical viewpoint in which Kripke structures become the objects of several categories while the morphisms are obtained from the corresponding notion of simulation. Here we define in detail sev...

A categorical outlook on relational modalities and simulations

We characterise bicategories of spans, relations and partial maps universally in terms of factorisations involving maps. We apply this characterisation to show that the standard modalities 2 and arise canonically as extensions of a predicate logic from functions to (abstract) relations. When relations and partial maps are representable, we exhibit logical predicates for the power-object and par...

Categorical Logic Categorical Logic

Categorical representations of categorical groups

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A simple example is computed in explicit detail.

Working Paper Series Categorical Data Categorical Data

Categorical outcome (or discrete outcome or qualitative response) regression models are models for a discrete dependent variable recording in which of two or more categories an outcome of interest lies. For binary data (two categories) probit and logit models or semiparametric methods are used. For multinomial data (more than two categories) that are unordered, common models are multinomial and...