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Core varieties, extensivity, and rig geometry

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F. William Lawvere

The role of the Frobenius operations in analyzing finite spaces, as
well as the extended algebraic geometry over rigs, depend partly on
varieties (Birkhoffian inclusions of algebraic categories) that have
coreflections as well as reflections and whose dual category of affine
spaces is extensive. Even within the category of those rigs where
1 + 1 =
1, not only distributive lattices but also the function algebras of
tropical geometry (where x + 1 = 1) and the dimension rigs of separable
prextensive categories (where x + x^2 = x^2) enjoy those features. (Talk
given at CT08, Calais.)

Keywords:
topos, Frobenius, dimension rigs

2000 MSC:
12F99, 18F10, 14A99

*Theory and Applications of Categories,*
Vol. 20, 2008,
No. 14, pp 497-503.

http://www.tac.mta.ca/tac/volumes/20/14/20-14.dvi

http://www.tac.mta.ca/tac/volumes/20/14/20-14.ps

http://www.tac.mta.ca/tac/volumes/20/14/20-14.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/14/20-14.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/14/20-14.ps

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