[FOM] Lambek's category of syntactic types

[Daniil]

This structure corresponds roughly to a residuated lattice, which I guess
can be seen as a decategorisation of a non-symmetric monoidal biclosed
category. Lambek himself explicitly mentions monoidal biclosed categories
in "Categorial and categorical grammars" (section 3).

What is that specifically you are interested in? Nowadays there is vast
amount of literature on type-logical grammar (what it is usually called
nowadays). There is a very nice book "Type-logical Semantics”, Bob
Carpenter – The MIT Press, 1997 on the topic. I should also direct you to a
chapter "Categorial type logics" by M. Moortgat.

Not related to natural languages, but to algebra behind this there is
“Residuated Lattices: An Algebraic Glimpse at Substructural Logics” by N.
Galatos, P. Jipsen, T. Kowalski, H. Ono, 2007.

Recently, there have been movements in the direction of incorporating
Lambek-style calculi into a symmetrical monoidal categories framework which
were recently applied to something to do with Quantum computing. I don't
know much about those developments, but a starting point can be:
http://arxiv.org/abs/1401.5980

Good luck.

-D
2016-04-15 17:04 GMT+02:00 Fosco <tetrapharmakon at gmail.com>:

> In the paper http://ling.umd.edu/~alxndrw/CGReadings/lambek-58.pdf the
> author seems to define a category whose objects are "syntactic types".
> One of the major point then is that this category is monoidal biclosed
> (see §7).
> (Even if the author never uses these words, it seems the most reasonable
> translation).
>
> I want to know more about this. Is there a literature I can consult?
> Thanks a lot
>
> Fosco Loregian
>
> --
>
> *======Au commencement tout était morne et informe.Le Géomètre dit: "Que
> la lumière soit! "Et les structures là par espèces perçoitdu chaos émergent
> attraits, contours et normes.(C. Ehresmann, 1965)*
>
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