Locating reaction with 2-categories

Locating reaction with 2-categories

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...

Names for Games: Locating 2 × 2 Games

Prisoner’s Dilemma, Chicken, Stag Hunts, and other two-person two-move (2 × 2) models of strategic situations have played a central role in the development of game theory. The Robinson–Goforth topology of payoff swaps reveals a natural order in the payoff space of 2 × 2 games, visualized in their four-layer “periodic table” format that elegantly organizes the diversity of 2 × 2 games, showing r...

2-C∗-Categories with non-simple units

The 2-categories of G-categories and of G-graded Categories Are 2-equivalent

Given a group G, we prove that the 2-category of small categories with G-action and G-equivariant functors is 2-equivalent to the 2-category of small Ggraded categories and degree-preserving functors.

Absolute Lax 2-categories

We have introduced, in a previous paper, the fundamental lax 2-category of a ‘directed space’ X. Here we show that, when X has a T1-topology, this structure can be embedded into a larger one, with the same objects (the points of X), the same arrows (the directed paths) and the same cells (based on directed homotopies of paths), but a larger system of comparison cells. The new comparison cells a...