Tuesday, June 14, 2011

Theory Update 86

Motives are usually discussed in connection with the old Feynman techniques, and in terms of the traditional concept of cohomology as a functor from a category of spaces to a suitable algebraic category. But their appearance in physics suggests associating universality for motives in terms of emergent geometries based on categorical polytopes. This is what we like to talk about here. Thus our physics category of motives cares not for arbitrary collections of classical spaces. It cares about the (operad) polytopes that axiomatise categories themselves, and about canonical arithmetic generators for algebras based on measurement operators. Polytopes occur in all dimensions and so, like an ordinary space in Grothendieck's sense, our categories like to be infinite dimensional, or at least three dimensional for braids!

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