Birkhoff's Theorem from a geometric perspective: A simple example
From Hilbert's theorem of zeroes, and from Noether's ideal theory, Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes, similar to their role in the original examples of algebraic geometry. I will describe a simple...
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Shahid Beheshti University
2016-02-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | http://www.cgasa.ir/article_12425_b4ce2ab0ae3a843f00ff011b054f918b.pdf |
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doaj-00aa632af3ac4139a310e2e6605943692020-11-24T21:16:50ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612016-02-01411812425Birkhoff's Theorem from a geometric perspective: A simple exampleF. William Lawvere0Department of Mathematics, University at Buffalo, Buffalo, New York 14260-2900, United States of America.From Hilbert's theorem of zeroes, and from Noether's ideal theory, Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes, similar to their role in the original examples of algebraic geometry. I will describe a simple example that illustrates some of the aspects of this relationship. The dualization from algebra to geometry in the basic Grothendieck spirit can be accomplished (without intervention of topological spaces) by the following method, known as Isbell conjugacy.http://www.cgasa.ir/article_12425_b4ce2ab0ae3a843f00ff011b054f918b.pdfGrothendieck spectrumCantorBooleHilbertBirkhoff: Existence and Sufficiency of generalized pointsReflexive Graphs |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
F. William Lawvere |
| spellingShingle |
F. William Lawvere Birkhoff's Theorem from a geometric perspective: A simple example Categories and General Algebraic Structures with Applications Grothendieck spectrum Cantor Boole Hilbert Birkhoff: Existence and Sufficiency of generalized points Reflexive Graphs |
| author_facet |
F. William Lawvere |
| author_sort |
F. William Lawvere |
| title |
Birkhoff's Theorem from a geometric perspective: A simple example |
| title_short |
Birkhoff's Theorem from a geometric perspective: A simple example |
| title_full |
Birkhoff's Theorem from a geometric perspective: A simple example |
| title_fullStr |
Birkhoff's Theorem from a geometric perspective: A simple example |
| title_full_unstemmed |
Birkhoff's Theorem from a geometric perspective: A simple example |
| title_sort |
birkhoff's theorem from a geometric perspective: a simple example |
| publisher |
Shahid Beheshti University |
| series |
Categories and General Algebraic Structures with Applications |
| issn |
2345-5853 2345-5861 |
| publishDate |
2016-02-01 |
| description |
From Hilbert's theorem of zeroes, and from Noether's ideal theory, Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes, similar to their role in the original examples of algebraic geometry. I will describe a simple example that illustrates some of the aspects of this relationship. The dualization from algebra to geometry in the basic Grothendieck spirit can be accomplished (without intervention of topological spaces) by the following method, known as Isbell conjugacy. |
| topic |
Grothendieck spectrum Cantor Boole Hilbert Birkhoff: Existence and Sufficiency of generalized points Reflexive Graphs |
| url |
http://www.cgasa.ir/article_12425_b4ce2ab0ae3a843f00ff011b054f918b.pdf |
| work_keys_str_mv |
AT fwilliamlawvere birkhoffstheoremfromageometricperspectiveasimpleexample |
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