Catégories de Peano et catégories algorithmiques, récursivité. (French) Zbl 0565.18004

Diagrammes 12, LC 1-LC 47 (1984).
The main aim of this paper is to give some definitions and results about recursion theory in an algebraic setting, in order to point out the role of categorical algebra in recursion theory. According to the author, a detailed study of more technical questions in recursion theory is not to be find here.
The paper is divided into four chapters. In chapters 1 and 3 Peano categories and recursive functions are introduced. In chapters 2 and 4 (which is claimed to be the more important) more particular questions, as Kan extensions, D-algebras and generating methods for partial structures are studied.
Reviewer: P.L.Ferrari


18B99 Special categories
18A15 Foundations, relations to logic and deductive systems
03D20 Recursive functions and relations, subrecursive hierarchies
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18D35 Structured objects in a category (MSC2010)
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