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Sur les produits tensoriels extérieurs de structures algébriques. (On exterior tensor products of algebraic structures). (French) Zbl 0577.18006

Diagrammes 14, 84 p. (1985).
The role of bicategories as a general context to study enriched category theory is now recognized. In particular this allows the simultaneous study of various mathematical structures (corresponding to the various objects of the bicategory) and the relations between them, like tensor products of such structures.
The author introduces an alternative notion called ”tensorial system” which he presents as ”very close” to that of a bicategory. It is indeed so close to it that its main advantage is probably the possibility of filling in pages just by transposing well-known properties of bicategories.
This thesis is essentially interested in the study of the tensor product of two structures or two algebras and it throws some new light on this last problem. But it is a pity that the author seems to ignore most of what has already been done on this problem in universal algebra or in the theory of bicategories.
Reviewer: F.Borceux

MSC:

18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
18C10 Theories (e.g., algebraic theories), structure, and semantics
Full Text: EuDML