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
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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},
publisher = {mathdoc},
volume = {105},
year = {1981},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/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/