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Polarized category theory, modules, and game semantics
Theory and applications of categories, Tome 18 (2007), pp. 4-101 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

Classification : 18D10, 18C50, 03F52, 68Q55, 91A05, 94A05
Keywords: polarized categories, polarized linear logic, game semantics, theory of communication 
@article{TAC_2007_18_a1,
     author = {J.R.B. Cockett and R.A.G. Seely},
     title = {Polarized category theory, modules, and game semantics},
     journal = {Theory and applications of categories},
     pages = {4--101},
     year = {2007},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2007_18_a1/}
}
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J.R.B. Cockett; R.A.G. Seely. Polarized category theory, modules, and game semantics. Theory and applications of categories, Tome 18 (2007), pp. 4-101. http://geodesic.mathdoc.fr/item/TAC_2007_18_a1/