The Block Product of Categories and Tilson's Division

Article type: Research Article

Authors: Rey, Jean-François

Affiliations: Institut Gaspard Monge. Université de Marne la Vallée., 2, rue de la Butte Verte. 93166 Noisy le Grand Cedex France. e-mail: jfrey@monge.univ-mlv.fr

Abstract: This paper introduces the notion of block product of two categories. It is the first step in the working out of a useful definition of the block product of two C-varieties which is needed for the theory of decompositions of monoids by means of wreath or block products. The construction of the block product of two categories is a particular case of a more general notion: the strong semidirect product of an action. In this first part of a two parts work we define the strong semidirect product functor and give some properties of this functor with respect to Tilson's division. In the second part we construct a left adjoint of the strong semidirect product functor and we define the kernel of a relational morphism of categories. With these notions we define the block product of two C-varieties and prove a kernel theorem in the category settings which extends a work of J. Rhodes and B. Tilson.

DOI: 10.3233/FI-1997-313409

Journal: Fundamenta Informaticae, vol. 31, no. 3-4, pp. 379-400, 1997