## Polarized category theory, modules, game semantics

**J.R.B. Cockett and R.A.G. Seely**
Motivated by an analysis of Abramsky-Jagadeesan games, the paper
considers a categorical semantics for a polarized notion of two-player
games, a semantics which has close connections with the logic of (finite
cartesian) sums and products, as well as with the multiplicative
structure of linear logic. In each case, the structure is polarized, in
the sense that it will be modelled by two categories, one for each of
two polarities, with a module structure connecting them. These are
studied in considerable detail, and a comparison is made with a
different notion of polarization due to Olivier Laurent: there is an
adjoint connection between the two notions.