A generalization of Zakrzewski morphisms

Abstract

The purpose of this paper is to generalize the notion of morphism introduced by Zakrzewski in [5]. In [2] we have proved that a morphism from Γ to G in the sense of Zakrzewski [5] can be viewed as a left action of Γ on G, which com- mutes with multiplication on G and in [1] we have proved that such a morphism is determined and determines a right action of Γ on G(o) and a groupoid homo- morphism from the action groupoid G(0) x Γ to G. In this paper a morphism from Γ to G will be given by a right Γ-space X and a groupoid homomorphism c : X [수식]Γ→ G. We shall prove that the class of groupoids as objects and the classes of equivalent morphisms (X; c) as arrows form a category [수식]. The isomorphisms of the resulted category [수식] can be viewed as the usual groupoid isomorphisms. Moreover we shall show that the category of groupoids as ob- jects and homomorphisms (in the usual sense) as arrows is equivalent with a subcategory of [수식.