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The Mathematics of Sentence Structure
The aim of this paper is to obtain an effective rule (or algorithm) for distinguishing sentences from nonsentences, which works not only for the formal languages of interest to the mathematicalExpand
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  • 134
  • PDF
Introduction to higher order categorical logic
Preface Part I. Introduction to Category Theory: Part II. Cartesian Closed Categories and Calculus: Part III. Type Theory and Toposes: Part IV. Representing Numerical Functions in Various CategoriesExpand
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Type Grammar Revisited
  • J. Lambek
  • Mathematics, Computer Science
  • LACL
  • 22 September 1997
TLDR
A protogroup is an ordered monoid in which each element a has both a left proto-inverse al such that ala ≤ 1 and a right protoinverse ar such that aar ≤ 1. Expand
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On the Calculus of Syntactic Types
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Lectures on Rings and Modules
This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with aExpand
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A fixpoint theorem for complete categories
  • 201
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Deductive systems and categories
  • J. Lambek
  • Mathematics, Computer Science
  • Mathematical systems theory
  • 1 December 1968
TLDR
We investigate the connection between proofs in certain deductive systems and canonical mappings in the category of categories. Expand
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Diagram chasing in Mal'cev categories
Abstract A diagram chasing technique generalizing the ‘two-square’ lemma of homological algebra is extended from Mal'cev varieties to Mal'cev categories: regular categories in which all reflexiveExpand
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