Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Fixed points in representations of categories

Authors: J. Adámek and J. Reiterman
Journal: Trans. Amer. Math. Soc. 211 (1975), 239-247
MSC: Primary 18A30
MathSciNet review: 0376799
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Abstract: Fixed points of endomorphisms of representations, i.e. functors into the category of sets, are investigated. A necessary and sufficient condition on a category K is given for each of its indecomposable representations to have the fixed point property. The condition appears to be the same as that found by Isbell and Mitchell for Colim: $ {\text{Ab}^K} \to {\text{Ab}}$ to be exact. A well-known theorem on mappings of Katětov and Kenyon is extended to transformations of functors.

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Article copyright: © Copyright 1975 American Mathematical Society