Geodesic
Dialectica and Chu Constructions: Cousins?
Theory and applications of categories, Chu spaces: theory and applications, Tome 17 (2006), pp. 127-152

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This note investigates two generic constructions used to produce categorical models of linear logic, the Chu construction and the Dialectica construction, in parallel. The constructions have the same objects, but are rather different in other ways. We discuss similarities and differences and prove that the Dialectica construction can be done over a symmetric monoidal closed basis. We also point out interesting open problems concerning the Dialectica construction.

Classification : 18C50, 18D10, 18D15, 03F52, 03F07
Keywords: linear logic, categorical models, monoidal closed categories, monoidal comonad, dialectica categories, chu spaces 
@article{TAC_2006_17_a6,
     author = {Valeria de Paiva},
     title = {Dialectica and {Chu} {Constructions:} {Cousins?}},
     journal = {Theory and applications of categories},
     pages = {127--152},
     publisher = {mathdoc},
     volume = {17},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2006_17_a6/}
}
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Valeria de Paiva. Dialectica and Chu Constructions: Cousins?. Theory and applications of categories, Chu spaces: theory and applications, Tome 17 (2006), pp. 127-152. http://geodesic.mathdoc.fr/item/TAC_2006_17_a6/