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.
Keywords: linear logic, categorical models, monoidal closed categories, monoidal comonad, dialectica categories, chu spaces
2000 MSC: 18C50, 18D10, 18D15, 03F52, 03F07
Theory and Applications of Categories,
Vol. 17, 2006,
No. 7, pp 127-152.
http://www.tac.mta.ca/tac/volumes/17/7/17-07.dvi
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http://www.tac.mta.ca/tac/volumes/17/7/17-07.pdf
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