Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(6): 1589-1600

Online first article August 6, 2019      Printed November 30, 2019

https://doi.org/10.4134/BKMS.b190016

Copyright © The Korean Mathematical Society.

Cocyclic morphism sets depending on a morphism in the category of pairs

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.