Morphisms of Open Games

Morphisms of open games

We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the more intuitively obvious definition of globular morphisms as mappings between strategy profiles that preserve best responses, and hence in particular preserve Nash equilibria. We construct a symmetric monoidal double category i...

Coalgebra Morphisms Subsume Open Maps

Open String Instantons and Relative Stable Morphisms

We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri and Vafa from the point of view of physics. By using the method of virtual localization, we successfully reproduce their results for multiple covers of a hol...

On Open-Open Games of Uncountable Length

The aim of this paper is to investigate the open-open game of uncountable length. We introduce a cardinal number μ X , which says how long the Player I has to play to ensure a victory. It is proved that c X ≤ μ X ≤ c X . We also introduce the class Cκ of topological spaces that can be represented as the inverse limit of κ-complete system {Xσ, π ρ ,Σ} with w Xσ ≤ κ and skeletal bonding maps. It ...

On morphisms of crossed polymodules

‎In this paper‎, ‎we prove that the category of crossed polymodules (i.e‎. ‎crossed modules of polygroups) and their morphisms is finitely complete‎. ‎We‎, ‎therefore‎, ‎generalize the group theoretical case of this completeness property of crossed modules‎.