Pairings in Categories

Abstract

We study a categorical generalization of some of the basic results of the homotopy theory which have been obtained in the category of topological spaces with base point. They are some of the results of Gottlieb, Hilton, Hoo, Lim, Varadarajan, Woo and Kim and others. To carry out categorical approach, we define pseudo-product, pseudo-coproduct and homotopy relation in general categories. These concepts enable us to define pairings and copairings in categories. Some of the classical results mentioned above are generalized to the categories with product, coproduct and zero object.