Timeline for Algebraic K-theory with commutative semirings?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 16, 2012 at 21:29 | vote | accept | Niemi | ||
| Aug 16, 2012 at 12:29 | history | edited | Jeffrey Giansiracusa |
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| Aug 16, 2012 at 8:37 | answer | added | Jeffrey Giansiracusa | timeline score: 9 | |
| Aug 16, 2012 at 6:07 | comment | added | K.J. Moi | People have certainly been interested in the categorified version of your question (jtopol.oxfordjournals.org/content/4/3/…). Do you have some more context for your question? Is there a particular category of modules or something that you want to understand? | |
| Aug 16, 2012 at 0:02 | comment | added | Fernando Muro | A trivial way to do it: define the $K$-theory of a semiring as the $K$-theory of the ring obtained by 'adding' additive inverses. I guess you may have some idea behing your question. Perhapes you should say someting about it in order to possible get interesting answers. | |
| Aug 15, 2012 at 22:37 | comment | added | user1437 | I dont know of any references, but at least one can say the obvious generalisation of higher K theory isnt as nice. The forgetful functor U Semiring to Set still has a left adjoint F and thus there is a cotriple FU. So for a semiring there is still a simplicial semiring, and one can apply the GL functor and take simplicial homotopy groups. The problem though is that GL is much less interesting for semirings. | |
| Aug 15, 2012 at 21:47 | history | asked | Niemi | CC BY-SA 3.0 |