We introduce the notion of *elementary Seely category* as a
notion of categorical model of Elementary Linear Logic (ELL)
inspired from Seely's definition of models of Linear Logic (LL).
In order to deal with additive connectives in ELL, we use the
approach of Danos and Joinet. From the categorical
point of view, this requires us to go outside the usual
interpretation of connectives by functors. The $!$ connective is
decomposed into a pre-connective $\sharp$ which is interpreted by a
whole family of functors (generated by $\id$, $\tens$ and $\with$).
As an application, we prove the stratified coherent model and the
obsessional coherent model to be elementary Seely categories and
thus models of ELL.

Keywords: monoidal categories, elementary linear logic, categorical logic, denotational semantics, coherent spaces

2000 MSC: 18C50

*Theory and Applications of Categories,*
Vol. 22, 2009,
No. 10, pp 269-301.

http://www.tac.mta.ca/tac/volumes/22/10/22-10.dvi

http://www.tac.mta.ca/tac/volumes/22/10/22-10.ps

http://www.tac.mta.ca/tac/volumes/22/10/22-10.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/10/22-10.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/10/22-10.ps

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/10/22-10.pdf