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Could anyone give a basic explanation about Tor functors and, particularly, any idea about how they might be useful for the description of natural language?

Javier Arias
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  • What? Are they totally useless or what? – Javier Arias Jan 16 '15 at 22:48
  • They are very useful for serious algebra, but not for "description of natural language". Why do you think that they might be useful, considering that you probably understand nothing about homological algebra? – Mister Benjamin Dover Jan 16 '15 at 23:16
  • Well, description of natural language in current linguistics is mad with algebraic tools, somewhat adapted to the field. Why do you think they are useless, considering you probably understand nothing about modern linguistics? – Javier Arias Jan 17 '15 at 09:32
  • This may be so, but to understand the Tor functors one needs some serious knowledge of algebra, which I guess most people working in your field don't have. (I am not talking about high school algebra.) In any case, if tensor products don't occur there, Tor functors are totally useless for this purpose. – Mister Benjamin Dover Jan 17 '15 at 11:36
  • Well, some linguists have used tensor products... – Javier Arias Jan 17 '15 at 11:53
  • In that case it would be good if you could give some links of applications of algebra in that field, in particular for tensor products – Mister Benjamin Dover Jan 17 '15 at 22:16
  • Here you have a basic report on the matter, including some specific link: http://www.quantuminteraction.org/applications/linguistics – Javier Arias Jan 18 '15 at 10:18
  • Do get a textbook on homological algebra. This is quite well explained in most (Well, not the connection with natural language, of course) – Mariano Suárez-Álvarez Jan 19 '15 at 21:22

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I am providing some evidence of the use of vectors in linguistic analysis, which might be a necessary assumption for the usage of tensors and then Tor-functors, as some user pointed out.

http://dl.acm.org/citation.cfm?id=1870773

Javier Arias
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    As far as I can see, that paper uses vector spaces and tensor products of tensor spaces (as a way to encode an analogue of entanglement) Tor functors simply will not be involved in that as they are all zero in that context. – Mariano Suárez-Álvarez Jan 19 '15 at 21:25
  • You mean entanglement as in quantum entanglement and the EPR paradox in Physics? What should happen for Tor functors to be involved then? – Javier Arias Jan 19 '15 at 21:32
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    I mean quantum entanglement —I do not mean at all any paradox, which probably has absolutely nothing to do with anything. Tor measures the failure of exactness of tensor products, and tensor products of vector spaces are exact, so there is nothing be be measured. As I wrote, you should consult any good textbook on homological algebra. – Mariano Suárez-Álvarez Jan 19 '15 at 21:37
  • Any recommendation? Any I could read online? – Javier Arias Jan 19 '15 at 21:38