Pairings on Lambda Algebras

✍ Scribed by W. S. Hatcher; Marcel Tonga

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 509 KB
• Volume: 37
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19910371908

✦ Synopsis

PAIRINGS ON LAMBDA ALGEBRAS by W. S. HATCHER in QuCbec (Canada) and MARCEL TONGA in Yaoundk (Cameroun)') This paper continues the authors' universal algebraic approach to the study of the I-calculus and its models begun in HATCHER and Scon [4], HATCHER and TONGA (61 and further developed in HATCHER and S c m [5], TONGA [lo], and more rcently HATCHER and TONGA [7],

which is essentially a resumk of some of the results presented in the present article.

The basic insight underlying our approach is that the traditional I-calculus is algebraically defective because it uses only one-half of the natural isomorphism A'' (A')', namely the right-hand side. The principal means of removing this defect is by an appropriate theory of pairings on so-called I-algebras and on the monoidal versions of these algebras. The goal of the present paper is to present such a theory.