Geodesic
The category of finite sets and Cartesian closed categories
Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part III, Tome 105 (1981), pp. 174-194
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Some universal properties of the category of finite sets with regard to Cartesian closed categories were studies. The equality of any two canonical morphisms (see Mac Lane[11]) in all Cartesian closed categories is redused to the equality of a finite number of maps in the category of finite sets. Hense, a new decision algorithm for equality of canonical morphisms has been obtained. Another, result is an algorithm to decide if two ($\&$, $\supset$)-formulas $A$ and $B$ are isomorphous in all Cartesian closed categories for any values of object-variables (where $\&$ is a cartesian product and $\supset$ is an internal hom-functor). The category of finite sets is used to prove the correctness of this algorithm. 
@article{ZNSL_1981_105_a8,
     author = {S. V. Solov'ev},
     title = {The category of finite sets and {Cartesian} closed categories},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {174--194},
     year = {1981},
     volume = {105},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_105_a8/}
}
TY  - JOUR
AU  - S. V. Solov'ev
TI  - The category of finite sets and Cartesian closed categories
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1981
SP  - 174
EP  - 194
VL  - 105
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1981_105_a8/
LA  - ru
ID  - ZNSL_1981_105_a8
ER  - 
%0 Journal Article
%A S. V. Solov'ev
%T The category of finite sets and Cartesian closed categories
%J Zapiski Nauchnykh Seminarov POMI
%D 1981
%P 174-194
%V 105
%U http://geodesic.mathdoc.fr/item/ZNSL_1981_105_a8/
%G ru
%F ZNSL_1981_105_a8
S. V. Solov'ev. The category of finite sets and Cartesian closed categories. Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part III, Tome 105 (1981), pp. 174-194. http://geodesic.mathdoc.fr/item/ZNSL_1981_105_a8/