Groupoidal relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner’s approach to deriving labelled bisimulation congruences from reduction systems. In this paper, we develop the theory of GRPOs further, proving that well-known equivalences, other than bisimulation, are congruences. To demonstrate the type of category theoretic arguments whi...

Recent advances in high throughput data acquisition and data storage technologies call for designing distributed agents that are able to learn This paper proposes a new abstract framework for modelling interactions among agents in multi-agent organizations. The proposed model – the model of interaction categories, or MIgories exhibits compositionality of interactions as well as emergence of beh...

Recently, symmetric categorical groups are used for the study of the Brauer groups of symmetric monoidal categories. As a part of these efforts, some algebraic structures of the 2-category of symmetric categorical groups SCG are being investigated. In this paper, we consider a 2-categorical analogue of an abelian category, in such a way that it contains SCG as an example. As a main theorem, we ...

We establish an equivalence of homotopy theories between symmetric monoidal bicategories and connective spectra. For this, we develop the theory of Γ-objects in 2-categories. In the course of the proof we establish strictfication results of independent interest for symmetric monoidal bicategories and for diagrams of 2-categories. CONTENTS

A Q-system in a C? 2-category is unitary version of separable Frobenius algebra object and can be viewed as higher idempotent. We define idempotent completion for 2-categories called study its properties. show that the right correspondences unital C?-algebras complete by constructing an inverse realization †-2-functor. use this result to construct induced actions group theoretical fusion catego...