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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
DOI: https://doi.org/10.1090/S0002-9947-1975-0376799-X
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.


References [Enhancements On Off] (What's this?)

  • [1] J. Adámek and J. Reiterman, Fixed-point property of unary algebras, Algebra Universalis 4 (1975), 163-165. MR 0357278 (50:9746)
  • [2] -, Exactness of the set-valued colim (manuscript).
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  • [7] S. Mac Lane, Categories for the working mathematician, Springer-Verlag, New York, 1972. MR 0354798 (50:7275)

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DOI: https://doi.org/10.1090/S0002-9947-1975-0376799-X
Article copyright: © Copyright 1975 American Mathematical Society

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