Tensor Product Functor

  • Thread starter nateHI
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At the risk of sounding ignorant I'd like to propose a question to someone well versed in Homological Algebra and General Relativity. I'm starting to study the tensor product functor in the context of category theory because I'm interested in possibly doing a paper on TQFT for a directed reading course. My question is, after working through the mathematics of the tensor functor how close will I be to being able to work out the mathematics of the Einstein Equations?

Edit/Addition: I guess my question should be, what is the relationship (if any) between the Tensor Product Functor from Category Theory and the Einstein Equations?
 
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mathwonk
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unfortunately I know nothing of general relativity or einstein's equations. but i know something about tensor product functors. they just express a way to linearize bilnear operations. (in mumbo jumbo talk, they represent the functor of bilinear maps, or equivalently, they turn the composition of two Hom functors into one Hom functor.) they are a certain mathematical language, whereas einstein's equations presumably say something in that language. so to me your question sounds sort of like asking whether after learning english one will be able to understand shakespeare. maybe, maybe not. as an aside, einstein did not have the abstract fomulation of tensor products as a functor i would guess, hence almost certainly used the more computational version of it.
 
  • #3
146
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unfortunately I know nothing of general relativity or einstein's equations. but i know something about tensor product functors. they just express a way to linearize bilnear operations. (in mumbo jumbo talk, they represent the functor of bilinear maps, or equivalently, they turn the composition of two Hom functors into one Hom functor.) they are a certain mathematical language, whereas einstein's equations presumably say something in that language. so to me your question sounds sort of like asking whether after learning english one will be able to understand shakespeare. maybe, maybe not. as an aside, einstein did not have the abstract fomulation of tensor products as a functor i would guess, hence almost certainly used the more computational version of it.
That's along the lines of what I was guessing. I suppose an idea for a paper would be to carry this line of thought out and make it precise. I suppose I would have to learn some GR which seems rather daunting.
 

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