This paper summarises recent results on bicategories of concurrent games and strategies. Nondeterministic concurrent strategies, those nondeterministic plays of a game left essentially unchanged by composition with copy-cat strategies, have recently been characterized as certain maps of event structures. This leads to a bicategory of general concurrent games in which the maps are nondeterminist...

Abstract In this paper, we discuss the generalization of finitary 2-representation theory 2-categories to birepresentation bicategories. previous papers on subject, classification simple transitive 2-representations a given 2-category was reduced that for certain subquotients. These reduction results were all formulated as bijections between equivalence classes 2-representations. generalize the...

In some bicategories, the 1-cells are ‘morphisms’ between the 0cells, such as functors between categories, but in others they are ‘objects’ over the 0-cells, such as bimodules, spans, distributors, or parametrized spectra. Many bicategorical notions do not work well in these cases, because the ‘morphisms between 0-cells’, such as ring homomorphisms, are missing. We can include them by using a p...

The goal of this paper is to provide the last equivalence needed in order identify all known models for ( ∞ , 2 ) $(\infty,2)$ -categories. We do by showing that Verity's model saturated 2-trivial complicial sets equivalent Lurie's $\infty$ -bicategories, which, turn, has been shown be other A key technical input given identifying notion -bicategories with weak a step which allows us understand...

The suspension loop construction is used to de ne a process in a symmetric monoidal category The algebra of such processes is that of symmetric monoidal bicategories Processes in categories with prod ucts and in categories with sums are studied in detail and in both cases the resulting bicategories of processes are equipped with opera tions called feedback Appropriate versions of traced monoida...

We study the monoidal structure of the standard strictification functor st : Bicat → 2Cat. In doing so, we construct monoidal structures on the 2-category whose objects are bicategories and on the 2-category whose objects are 2-categories.