Pairings in Categories | Zendy

Nobuyuki Oda | Zendy

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Pairings in Categories

Author(s) -

Nobuyuki Oda

Publication year - 1993

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195166744

Subject(s) - mathematics , coproduct , homotopy , categorical variable , generalization , product (mathematics) , object (grammar) , homotopy category , pure mathematics , base (topology) , algebra over a field , artificial intelligence , mathematical analysis , computer science , geometry , statistics

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.

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