Index of pdf files

This site contains Lambek's recent papers, nearly all written in this millennium. They are mostly undated, so I have sorted them by subject matter, which mostly breaks up into linguistics, physics, and category theory. Most of the category theory was for the linguistics. Some of the papers are not complete, since I got them from his typist. Some were published (and I have provided the citations) and some are not. Among the unpublished, most are undated and a couple seem to be duplicates, doubtless revisions. If anyone figures out which the latest version is, I will try to remove the duplicates. If I was able to download the actual publication, it appears as a normal citation. If the citation is preceded by "Appeared in:", I was not able to download the actual publication, but I compiled and included the source file for what may not be the final version. Dates of writing or of appearance are provided when discernible. All in all it is a remarkable amount of writing for someone aged between 75 and 90. According to MathSciNet, he had 19 publications between 2001 and 2013.

Michael Barr (






J. Lambek, Closed monoidal categories from linguistics to physics.

J. Lambek, Remarks on the history of categorial grammar.

J. Lambek, The syntax-semantics interface and the origins of philosophy.

J. Lambek, From rules of grammar to laws of nature. A mix of linguistics and philosophy

J. Lambek, From word to sentence: a pregroup analysis of the object pronoun who(m).

J. Lambek, Pregroups and natural language processing

J. Lambek, Capulet semantics and the prehistory of mathematics and science This is evidently an alternative to Montague semantics.

J. Lambek, Reflections on English personal pronouns.

J. Lambek, Invisible endings of English adjectives and nouns.

J. Lambek, A computational algebraic approach to English grammar.

Joachim Lambek and Noson Yanofsky, A Computational Approach to Biblical Hebrew Conjugation. In: Computational Algebraic Approaches to Natural Language, Edited by C. Casadio and J. Lambek. Polimetrica, Monza (Milan), Feburary, 2005.

D. Bargelli and J. Lambek, An algebraic approach to French sentence structure.

J. Lambek, Exploring feature agreement in French with parallel pregroup computations. Probably an earlier version of paper of the same name dated 2008.

D. Bargelli and J. Lambek, An algebraic approach to Arabic sentence structure (2003).

J. Lambek, Iterated Galois connections in arithmetic and linguistics.

Claudia Casadio and Joachim Lambek, A tale of four grammars: The Lambek calculus in logic and linguistics. Studia Logica 71 (2002), 315–329.

J. Lambek, Should pregroup grammars be adorned with additional operations? Studia Logica 87 (2007), no. 2-3, 343–358.

J. Lambek, Exploring feature agreement in French with parallel pregroup computations (2008).

J. Lambek, Pregroup grammars and Chomsky’s earliest examples. J. Log. Lang. Inf. 17 (2008), no. 2, 141–160.

J. Lambek, From word to sentence: a computational approach to grammar (2008).

Joachim Lambek, Logic and grammar. Studia Logica 100 (2012), 667–681.


J. Lambek, Compact monoidal categories from linguistics to physics. . New structures for physics, 467–487, Lecture Notes in Phys., 813, Springer, Heidelberg, 2011.

J. Lambek, A six-vector classification of fundamental particles (2013).

J. Lambek, Six-dimensional Lorentz category (2012). With an intro by R.A.G. Seely. This is to be published in: "Categories for the Working Philosopher", edited by Elaine Landry, and to be published by Oxford University Press.

J. Lambek, The Lorentz category in special relativity. This appeared in: Models, logics, and higher-dimensional categories, 169–175, CRM Proc. Lecture Notes, 53, Amer. Math. Soc., Providence, RI, 2011.

Joachim Lambek, In praise of quaternions. This is apparently the original of a published article of the same name: C. R. Math. Acad. Sci. Soc. R. Can. 35 (2013), no. 4, 121–136. I have added an appendix giving an algebraic description of biquaternions (which is what the paper is really about).

Joachim Lambek, Quaternions and three temporal dimensions (2014).


Anne Preller and Joachim Lambek, Free compact 2-categories. Math. Structures Comput. Sci. 17 (2007), no. 2, 309–340.

J. Lambek, Bicategories in algebra and linguistics. Appeared in: Linear logic in computer science, 325–345, London Math. Soc. Lecture Note Ser., 316, Cambridge Univ. Press, Cambridge, 2004.

J. Lambek, Recollections of a reluctant categorist.

Joachim Lambek, Michael Barr, John Kennison, and Robert Raphael, Injective hulls of partially ordered monoids. Theory Appl. Categories. 26 (2012), 338–348.

Joachim Lambek and Philip J. Scott, Lambek, Joachim; Scott, Reflections on the categorical foundations of mathematics. Foundational theories of classical and constructive mathematics, 171–186, West. Ont. Ser. Philos. Sci., 76, Springer, Dordrecht, 2011.


J. Lambek, What is the world of mathematics? This appeared under an extended title in: Ann. Pure Appl. Logic 126 (2004), no. 1-3, 149–158.

J. Lambek, Programs, grammars, arguments. These are unpublished course notes (augmented by a chapter on the French verb) used for many years as the basis of a course called "Computability and mathematical linguistics" that combined Jim's very early works on register machines with those on formal grammars.

Joachim Lambek and Philip Scott, An exactification of the monoid of primitive recursive functions. Studia Logica 81 (2005), no. 1, 1–18.

J. Lambek, Discrete versus continuous and the radical approach to infinitesimals (2007). This presumably is an earlier version of: The radical approach to infinitesimals in historical perspective. C. R. Math. Acad. Sci. Soc. R. Can. 34 (2012), no. 1, 9–22, which lies behind a paywall.

J. Lambek, The radical approach to infinitesimals in historical perspective (2007). Presumably another early version of the published work just cited.

Joachim Lambek Relations old and new. Relational methods for computer science applications, Stud. Fuzziness Soft Comput., 65, 135–147, Physica, Heidelberg, 2001.

June 23, 2015