Implementing finite structures in Mathematica via a skeletal topos of finite sets

✍ Scribed by Susan B. Niefield

• Book ID: 104344803
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 165 KB
• Volume: 35
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1016/s0747-7171(02)00105-0

✦ Synopsis

To implement finite structures in a symbolic computation program such as Mathematica, we consider a skeletal topos N which is equivalent to the category Set f of finite sets. Objects of N are nonnegative integers, and morphisms f :

for all i. A full and faithful functor from N to Set f is obtained by identifying n with the set [n] = {1, . . . , n} and identifying ( f 1 , . . . , f n ) with the function i → f i . A topos structure on N (appropriate for Mathematica) is obtained by transporting the topos structure of Set f along a suitable pseudo-inverse C of the functor from N to Set f described above. The code for the Mathematica implementation included below is also available as a Mathematica Notebook.