Arcadian Functor

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Marni D. Sheppeard

Tuesday, April 17, 2007

M Theory Lesson 40

The misuse of common terms may be getting a little out of hand here. We may need to begin inventing words. Let us introduce the term n-logos. This is supposed to be reminiscent of the term n-topos, but more emphasis is being placed on generalised logic.

A 1-logos is like a sheaf, and a 2-logos is more commonly known as a topos (with extra stuff). It is 2-dimensional because it hinges on diagrams made up from squares. As we have found, the structure we need to understand M theory is a 3-logos. This uses parity cubes instead of parity squares, and ternary logic instead of binary logic.

Note that a 2-logos is like a category of 1-logoses, because the canonical example is the topos Set of sets, which are sheaves over a point. But we are defining n-logoses prior to defining categories, which are simply algebras arising from operads. And whereas categories have Euler characteristics, logoses have zeta functions.


Blogger L. Riofrio said...

This n-logos term could catch on. Did you invent it? Maybe they will name it for you.

April 18, 2007 4:23 AM  
Blogger Kea said...

Hi Louise! Yes, I invented it just now, but language (or indeed mathematics) is not my strong point.

April 18, 2007 11:15 AM  

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