A 2-categorical state sum model

Auditing Categorical SUM, MAX and MIN Queries

Auditing consists in logging answered queries and checking, each time that a new query is submitted, that no sensitive information is disclosed by combining responses to answered queries with the response to the current query. Such a method for controlling data disclosure naturally raises the following inference problem: Given a set Q of answered queries and a query q, is the information asked ...

A Double Categorical Model of Weak 2-categories

We introduce the notion of weakly globular double categories, a particular class of strict double categories, as a way to model weak 2-categories. We show that this model is suitably equivalent to bicategories and give an explicit description of the functors involved in this biequivalence. As an application we show that groupoidal weakly globular double categories model homotopy 2-types.

A Categorical Model for Context

state-sum models and gerbes

where G is a finite group. If we want to understand the differential geometry behind the DW-model we have to give up the finiteness of G of course. If G is a Lie group, we can ask ourselves what geometric objects correspond to smooth homomorphisms from π1(M) to G (we will not explain here what we mean by smoothness exactly). The answer is well known: principal Gbundles with flat connections. We...

Deriving Bisimulation Congruences: A 2-categorical Approach

We introduce G-relative-pushouts (GRPO) which are a 2-categorical generalisation of relative-pushouts (RPO). They are suitable for deriving labelled transition systems (LTS) for process calculi where terms are viewed modulo structural congruence. We develop their basic properties and show that bisimulation on the LTS derived via GRPOs is a congruence, provided that sufficiently many GRPOs exist...