Jiyean Kim, Kee Young Lee Korea University, Korea University
Abstract : In this paper, we apply the notion of cocyclic maps to the category of pairs proposed by Hilton and obtain more general concepts. We discuss the concept of cocyclic morphisms with respect to a morphism and find that it is a dual concept of cyclic morphisms with respect to a morphism and a generalization of the notion of cocyclic morphisms with respect to a map. Moreover, we investigate its basic properties including the preservation of cocyclic properties by morphisms and find conditions for which the set of all homotopy classes of cocyclic morphisms with respect to a morphism will have a group structure.
Keywords : cocyclic map, cocyclic morphism, category of pairs
MSC numbers : Primary 55Q05; Secondary 55P30
Supported by : This work was supported by a Korea University Grant.