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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.
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참고문헌 (12)
참고문헌 신청
D. H. Gottlieb / 1965 / A Certain Subgroup of the Fundamental Group / American Journal of Mathematics 87(4):840~856
Daniel Henry Gottlieb / 1969 / Evaluation Subgroups of Homotopy Groups / American Journal of Mathematics 91(3):729~756
P. Hilton / 1965 / Homotopy Theory and Duality / Gordon and Breach Science Publishers
김지연 / 2010 / GOTTLIEB SUBSETS WITH RESPECT TO A MORPHISM IN THE CATEGORY OF PAIRS / 대한수학회보 47(6):1311~1327
K. Y. Lee / 1998 / Cyclic morphisms in the category of pairs and generalized G-sequences / J. Math. Kyoto Univ 38(2):271~285
Daniel Henry Gottlieb / 1969 / Evaluation Subgroups of Homotopy Groups / American Journal of Mathematics 91(3):729~756
P. Hilton / 1965 / Homotopy Theory and Duality / Gordon and Breach Science Publishers
김지연 / 2010 / GOTTLIEB SUBSETS WITH RESPECT TO A MORPHISM IN THE CATEGORY OF PAIRS / 대한수학회보 47(6):1311~1327
K. Y. Lee / 1998 / Cyclic morphisms in the category of pairs and generalized G-sequences / J. Math. Kyoto Univ 38(2):271~285
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